{"page":"\u003clink rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/resources-c03aa079.css\" /\u003e\n\u003clink rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/lp_boclips_stylesheets-517835be.css\" media=\"all\" /\u003e\n\u003cdiv data-title='Solving Simultaneous Equations By Substitution' data-url='/boclips/videos/634c0712e5f7455d0b8063ac' data-video-url='/boclips/videos/634c0712e5f7455d0b8063ac' id='bo_player_modal'\u003e\n\u003cdiv class='boclips-resource-page modal-dialog panel-container'\u003e\n\u003cdiv class='react-notifications-root'\u003e\u003c/div\u003e\n\u003cdiv class='rp-header'\u003e\n\u003cdiv class='rp-type'\u003e\n\u003ci aria-hidden='true' class='fai fa-regular fa-circle-play'\u003e\u003c/i\u003e\nVideo\n\u003c/div\u003e\n\u003ch1 class='rp-title' id='video-title'\u003e\nSolving Simultaneous Equations By Substitution\n\u003c/h1\u003e\n\u003cdiv class='rp-actions'\u003e\n\u003cdiv class='mr-1'\u003e\n\u003ca class=\"btn btn-success\" data-posthog-event=\"Signup: LP Signup Activity\" data-posthog-location=\"body_link_boclips\" data-remote=\"true\" href=\"/subscription/new\"\u003e\u003cspan\u003e\u003cspan\u003eGet Free Access\u003c/span\u003e\u003cspan class=\"\"\u003e for 10 Days\u003c/span\u003e\u003cspan\u003e!\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv class='rp-body'\u003e\n\u003cdiv class='rp-info'\u003e\n\u003cdiv aria-label='Hide resource details' class='rp-hide-info' role='button' tabindex='0'\u003e\u0026times;\u003c/div\u003e\n\u003ci aria-label='Expand resource details' class='rp-expand-info fai fa-solid fa-up-right-and-down-left-from-center' role='button' tabindex='0'\u003e\u003c/i\u003e\n\u003ci aria-label='Compress resource details' class='rp-compress-info fai fa-solid fa-down-left-and-up-right-to-center' role='button' tabindex='0'\u003e\u003c/i\u003e\n\u003cdiv class='rp-rating'\u003e\n\u003cspan class='resource-pool'\u003e\n\u003cspan class='pool-label'\u003ePublisher:\u003c/span\u003e\n\u003cspan class='pool-name'\u003e\n\u003cspan class='text'\u003e\u003ca data-publisher-id=\"30356647\" href=\"/search?publisher_ids%5B%5D=30356647\"\u003eFuseSchool\u003c/a\u003e\u003c/span\u003e\n\u003c/span\u003e\n\u003c/span\u003e\n\u003c/div\u003e\n\u003cdiv class='rp-description'\u003e\n\u003cspan class='short-description'\u003eIn this video we are going to discover how to solve simultaneous equations by substitution. Simultaneous equations are two or more equations with two or more unknowns that must be solved at the same time; hence the name simultaneous....\u003c/span\u003e\n\u003cspan class='full-description hide'\u003eIn this video we are going to discover how to solve simultaneous equations by substitution. Simultaneous equations are two or more equations with two or more unknowns that must be solved at the same time; hence the name simultaneous. \u003cbr/\u003e\u003cbr/\u003eThere are three different methods for solving simultaneous equations: elimination, substitution and graphically. Elimination doesn’t always work and solving graphically is slow and not accurate. Solving them using substitution does always work, which we will look at in this video. \u003cbr/\u003e\u003cbr/\u003eWhen we solve simultaneous equations, we may get one solution, like with linear equations, or if a quadratic is involved, we may get two solutions. And we might also get 2 solutions with a straight line and a circle. Before we start, we need to know what linear equations look like: they are equations with an ‘x’ and a ‘y’ in, or an ‘a’ and ‘b’, but no squared or cubed letters. \u003cbr/\u003e\u003cbr/\u003eTo solve simultaneous equations by substitution, start by rearranging the linear equation to become y=. E.g. y = x + 3. We can now substitute this y= into the non-linear equation. So in place of the y in the non-linear equation, we write x+3 instead. x + 3 = x^2 + 1. Rearrange this to get a quadratic, then factorise and solve it. This gives two x values: x = -1 and x = 2. Because we have 2 x-values, we’ll need 2 y-values. Substitute the x-values into the linear y equals equation y = x + 3. So when x = -1, y = 2. And when x = 2, y = 5. So the solutions are (-1, 2) and (2, 5). \u003cbr/\u003e\u003cbr/\u003eAs always with maths, we should double check our answers. Substitute the solutions (-1, 2) and (2, 5) into the non-linear equation that was given in the question. \u003cbr/\u003e\u003cbr/\u003eSo there we have solving simultaneous equations by substitution. Take your time with the algebra, and always double check your answer at the end. Substitution will always work, whereas elimination won’t always. \u003cbr/\u003e\u003cbr/\u003eWhich is why some people choose to use substitution for any simultaneous equations, even if they are easy linear ones.\u003c/span\u003e\n\u003c/div\u003e\n\u003cdiv class='action-container flex justify-between'\u003e\n\u003cbutton aria-expanded='false' aria-label='Read more description' class='rp-full-description' type='button'\u003e\n\u003ci class='fai fa-solid fa-align-left'\u003e\u003c/i\u003e\n\u003cspan id='read_more'\u003eRead More\u003c/span\u003e\n\u003c/button\u003e\n\u003cdiv class='rp-report'\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv aria-labelledby='resource-details-heading' class='rp-info-section'\u003e\n\u003ch2 class='title' id='resource-details-heading'\u003eResource Details\u003c/h2\u003e\n\u003cdiv class='rp-resource-details clearfix'\u003e\n\u003cdiv class='detail'\u003e\n\u003cdl\u003e\n\u003cdt\u003eCurator Rating\u003c/dt\u003e\n\u003cdd\u003e\u003cspan class=\"star-rating\" aria-label=\"4.5 out of 5 stars\" role=\"img\"\u003e\u003ci class=\"fa-solid fa-star text-action\" aria-hidden=\"true\"\u003e\u003c/i\u003e\u003ci class=\"fa-solid fa-star text-action\" aria-hidden=\"true\"\u003e\u003c/i\u003e\u003ci class=\"fa-solid fa-star text-action\" aria-hidden=\"true\"\u003e\u003c/i\u003e\u003ci class=\"fa-solid fa-star text-action\" aria-hidden=\"true\"\u003e\u003c/i\u003e\u003ci class=\"fa-solid fa-star-half-stroke text-action\" aria-hidden=\"true\"\u003e\u003c/i\u003e\u003c/span\u003e\u003c/dd\u003e\n\u003c/dl\u003e\n\u003c/div\u003e\n\u003cdiv class='detail'\u003e\n\u003cdl\u003e\n\u003cdt class=\"educator-rating-title\"\u003eEducator Rating\u003c/dt\u003e\u003cdd\u003e\u003cdiv class=\"educator-rating-details\" data-path=\"/educator_ratings/rrp_data?resourceable_id=28370\u0026amp;resourceable_type=Boclips%3A%3AVideoMetadata\"\u003e\u003cspan class=\"not-yet-rated\"\u003eNot yet Rated\u003c/span\u003e\u003c/div\u003e\u003c/dd\u003e\n\u003c/dl\u003e\n\u003c/div\u003e\n\u003cdiv class='detail'\u003e\n\u003cdl\u003e\n\u003cdt\u003eMedia Length\u003c/dt\u003e\n\u003cdd\u003e3:53\u003c/dd\u003e\n\u003c/dl\u003e\n\u003c/div\u003e\n\u003cdiv class='detail'\u003e\n\u003cdl\u003e\n\u003cdt\u003eGrade\u003c/dt\u003e\u003cdd title=\"Grade\"\u003e6th - Higher Ed\u003c/dd\u003e\n\u003c/dl\u003e\n\u003c/div\u003e\n\u003cdiv class='detail'\u003e\n\u003cdl\u003e\n\u003cdt\u003eSubjects\u003c/dt\u003e\u003cdd\u003e\u003cspan\u003e\u003ca href=\"/search?grade_ids%5B%5D=258\u0026amp;grade_ids%5B%5D=259\u0026amp;grade_ids%5B%5D=252\u0026amp;grade_ids%5B%5D=253\u0026amp;grade_ids%5B%5D=254\u0026amp;grade_ids%5B%5D=255\u0026amp;grade_ids%5B%5D=256\u0026amp;grade_ids%5B%5D=257\u0026amp;search_tab_id=1\u0026amp;subject_ids%5B%5D=365220\"\u003eMath\u003c/a\u003e\u003c/span\u003e\u003c/dd\u003e\u003cdd class=\"text-muted\"\u003e\u003ci class=\"fa-solid fa-lock mr5\"\u003e\u003c/i\u003e10 more...\u003c/dd\u003e\n\u003c/dl\u003e\n\u003c/div\u003e\n\u003cdiv class='detail'\u003e\n\u003cdl\u003e\n\u003cdt\u003eMedia Type\u003c/dt\u003e\u003cdd\u003e\u003cspan\u003e\u003ca href=\"/search?grade_ids%5B%5D=258\u0026amp;grade_ids%5B%5D=259\u0026amp;grade_ids%5B%5D=252\u0026amp;grade_ids%5B%5D=253\u0026amp;grade_ids%5B%5D=254\u0026amp;grade_ids%5B%5D=255\u0026amp;grade_ids%5B%5D=256\u0026amp;grade_ids%5B%5D=257\u0026amp;search_tab_id=2\u0026amp;type_ids%5B%5D=4543647\"\u003eInstructional Videos\u003c/a\u003e\u003c/span\u003e\u003c/dd\u003e\n\u003c/dl\u003e\n\u003c/div\u003e\n\u003cdiv class='detail'\u003e\n\u003cdl\u003e\n\u003cdt\u003eSource:\u003c/dt\u003e\n\u003cdiv class='preview-source' data-animation='true' data-boundary='.rp-info' data-container='.rp-resource-details' data-html='false' data-title='Education for anyone, anywhere' data-trigger='hover focus'\u003e\n\u003cspan\u003eFuseSchool - Global Education\u003c/span\u003e\n\u003ci aria-hidden='true' class='fa-solid fa-circle-info channel-tooltip-icon' id='channel-tooltip'\u003e\u003c/i\u003e\n\u003c/div\u003e\n\u003c/dl\u003e\n\u003c/div\u003e\n\u003cdiv class='detail'\u003e\n\u003cdl\u003e\n\u003cdt\u003eDate\u003c/dt\u003e\n\u003cdd\u003e2017\u003c/dd\u003e\n\u003c/dl\u003e\n\u003c/div\u003e\n\u003cdiv class='detail'\u003e\n\u003cdl\u003e\n\u003ci aria-hidden='true' class='fai fa-solid fa-language'\u003e\u003c/i\u003e\n\u003cdt\u003eLanguage\u003c/dt\u003e\u003cdd\u003eEnglish\u003c/dd\u003e\n\u003c/dl\u003e\n\u003c/div\u003e\n\u003cdiv class='detail'\u003e\n\u003cdl\u003e\n\u003cdt\u003eAudiences\u003c/dt\u003e\u003cdd\u003e\u003cspan\u003e\u003ca href=\"/search?audience_ids%5B%5D=371079\u0026amp;grade_ids%5B%5D=258\u0026amp;grade_ids%5B%5D=259\u0026amp;grade_ids%5B%5D=252\u0026amp;grade_ids%5B%5D=253\u0026amp;grade_ids%5B%5D=254\u0026amp;grade_ids%5B%5D=255\u0026amp;grade_ids%5B%5D=256\u0026amp;grade_ids%5B%5D=257\u0026amp;search_tab_id=1\"\u003eFor Teacher Use\u003c/a\u003e\u003c/span\u003e\u003c/dd\u003e\u003cdd class=\"text-muted\"\u003e\u003ci class=\"fa-solid fa-lock mr5\"\u003e\u003c/i\u003e2 more...\u003c/dd\u003e\n\u003c/dl\u003e\n\u003c/div\u003e\n\u003cdiv class='detail'\u003e\n\u003cdl\u003e\n\u003cdt\u003eUsage Permissions\u003c/dt\u003e\u003cdd\u003eFine Print: Educational Use\u003c/dd\u003e\n\u003c/dl\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv aria-labelledby='additional-materials-heading' class='rp-info-section'\u003e\n\u003ch2 class='title' id='additional-materials-heading'\u003eAdditional Materials\u003c/h2\u003e\n\u003cdiv class='additional-material'\u003e\n\u003ci aria-hidden='true' class='fai fa-solid fa-lock'\u003e\u003c/i\u003e\n\u003ca class=\"text-muted\" title=\"Video Transcript\" data-html=\"true\" data-placement=\"bottom\" data-trigger=\"click\" data-content=\"\u003cdiv class=\u0026quot;text-center py-2\u0026quot;\u003e\u003ca class=\u0026quot;bold\u0026quot; href=\u0026quot;/auth/users/sign_in\u0026quot;\u003eSign in\u003c/a\u003e or \u003ca class=\u0026quot;bold text-danger\u0026quot; data-posthog-event=\u0026quot;Signup: LP Signup Activity\u0026quot; data-posthog-location=\u0026quot;body_link_boclips\u0026quot; data-remote=\u0026quot;true\u0026quot; href=\u0026quot;/subscription/new\u0026quot;\u003eJoin Now\u003c/a\u003e\u003c/div\u003e\" data-title=\"Get Full Access\" data-container=\"body\" rel=\"popover\" tabindex=\"0\" href=\"/subscription/new\"\u003eVideo Transcript\u003c/a\u003e\n\u003c/div\u003e\n\u003cdiv class='additional-material'\u003e\n\u003ci aria-hidden='true' class='fai fa-solid fa-lock'\u003e\u003c/i\u003e\n\u003ca class=\"text-muted\" title=\"Video Preview\" data-html=\"true\" data-placement=\"bottom\" data-trigger=\"click\" data-content=\"\u003cdiv class=\u0026quot;text-center py-2\u0026quot;\u003e\u003ca class=\u0026quot;bold\u0026quot; href=\u0026quot;/auth/users/sign_in\u0026quot;\u003eSign in\u003c/a\u003e or \u003ca class=\u0026quot;bold text-danger\u0026quot; data-posthog-event=\u0026quot;Signup: LP Signup Activity\u0026quot; data-posthog-location=\u0026quot;body_link_boclips\u0026quot; data-remote=\u0026quot;true\u0026quot; href=\u0026quot;/subscription/new\u0026quot;\u003eJoin Now\u003c/a\u003e\u003c/div\u003e\" data-title=\"Get Full Access\" data-container=\"body\" rel=\"popover\" tabindex=\"0\" href=\"/subscription/new\"\u003eVideo Preview\u003c/a\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv aria-labelledby='concepts-heading' class='rp-info-section'\u003e\n\u003ch2 class='title' id='concepts-heading'\u003eConcepts\u003c/h2\u003e\n\u003cdiv class='clearfix'\u003e\n\u003cdiv class='details-list concepts' data-identifier='Boclips::VideoDecorator634c0712e5f7455d0b8063ac' data-type='concepts'\u003esubstitution, solutions, linear, equations, values, time, work, roots, graphs\u003c/div\u003e\n\u003cdiv class='concepts-toggle-buttons' data-identifier='Boclips::VideoDecorator634c0712e5f7455d0b8063ac'\u003e\n\u003cbutton aria-expanded='false' class='more btn-link' type='button'\u003e\n\u003cspan\u003eShow More\u003c/span\u003e\n\u003ci aria-hidden='true' class='fa-solid fa-caret-down ml5'\u003e\u003c/i\u003e\n\u003c/button\u003e\n\u003cbutton aria-expanded='true' class='less btn-link' style='display: none;' type='button'\u003e\n\u003cspan\u003eShow Less\u003c/span\u003e\n\u003ci aria-hidden='true' class='fa-solid fa-caret-up ml5'\u003e\u003c/i\u003e\n\u003c/button\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv aria-labelledby='additional-tags-heading' class='rp-info-section'\u003e\n\u003ch2 class='title' id='additional-tags-heading'\u003eAdditional Tags\u003c/h2\u003e\n\u003cdiv class='clearfix'\u003e\n\u003cdiv class='details-list keyterms' data-identifier='Boclips::VideoDecorator634c0712e5f7455d0b8063ac' data-type='keyterms'\u003emaths, digital learning, online learning, learn maths, school maths, mathematics, gcse maths, high school maths, maths help, free online education, fuseschool, fuse school, algebra, simultaneous equations, elimination, solve equations, solving, linear equation, nonlinear equation, double check, click play, equals, video, discover, solve, solution, quadratic, circle, start, substitute, answers, pause, find, ready\u003c/div\u003e\n\u003cdiv class='keyterms-toggle-buttons' data-identifier='Boclips::VideoDecorator634c0712e5f7455d0b8063ac'\u003e\n\u003cbutton aria-expanded='false' class='more btn-link' type='button'\u003e\n\u003cspan\u003eShow More\u003c/span\u003e\n\u003ci aria-hidden='true' class='fa-solid fa-caret-down ml5'\u003e\u003c/i\u003e\n\u003c/button\u003e\n\u003cbutton aria-expanded='true' class='less btn-link' style='display: none;' type='button'\u003e\n\u003cspan\u003eShow Less\u003c/span\u003e\n\u003ci aria-hidden='true' class='fa-solid fa-caret-up ml5'\u003e\u003c/i\u003e\n\u003c/button\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv aria-labelledby='classroom-considerations-heading' class='rp-info-section'\u003e\n\u003ch2 class='title' id='classroom-considerations-heading'\u003eClassroom Considerations\u003c/h2\u003e\n\u003cdiv class='classroom-considerations'\u003e\u003cdiv class='fai fa-solid fa-bell'\u003e\u003c/div\u003eBest For: Explaining a topic\u003c/div\u003e\u003cdiv class='classroom-considerations'\u003e\u003cdiv class='fai fa-solid fa-bell'\u003e\u003c/div\u003eVideo is ad-free\u003c/div\u003e \n\u003c/div\u003e\n\u003cdiv aria-labelledby='educator-ratings-heading' class='rp-info-section'\u003e\n\u003ch2 class='title sr-only' id='educator-ratings-heading'\u003eEducator Ratings\u003c/h2\u003e\n\u003cdiv id=\"educator-ratings-root\"\u003e\u003c/div\u003e\u003cdiv id=\"all-educator-ratings-root\"\u003e\u003c/div\u003e\u003cdiv id=\"educator-rating-form-root\"\u003e\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv class='rp-resource'\u003e\n\u003cdiv aria-label='Show resource details' class='rp-show-info' role='button' tabindex='0'\u003e\n\u003ci class='fai fa-solid fa-align-left'\u003e\u003c/i\u003e\nShow resource details\n\u003c/div\u003e\n\u003cdiv aria-label='Video player' class='player' id='player-wrapper' role='region'\u003e\n\u003cdiv class='relative container mx-auto' id='lp-boclips-visitor-thumbnail'\u003e\n\u003ca class=\"block\" data-html=\"true\" data-placement=\"bottom\" data-trigger=\"click\" data-content=\"\u003cdiv class=\u0026quot;text-center py-2\u0026quot;\u003e\u003ca class=\u0026quot;bold\u0026quot; href=\u0026quot;/auth/users/sign_in\u0026quot;\u003eSign in\u003c/a\u003e or \u003ca class=\u0026quot;bold text-danger\u0026quot; data-posthog-event=\u0026quot;Signup: LP Signup Activity\u0026quot; data-posthog-location=\u0026quot;body_link_boclips\u0026quot; data-remote=\u0026quot;true\u0026quot; href=\u0026quot;/subscription/new\u0026quot;\u003eJoin Now\u003c/a\u003e\u003c/div\u003e\" data-title=\"Get Full Access\" data-container=\"body\" rel=\"popover\" tabindex=\"0\" aria-label=\"Play video: Solving Simultaneous Equations By Substitution\" href=\"/subscription/new\"\u003e\u003cimg class=\"resource-img img-thumbnail img-responsive z-10 lp-boclips-thumbnail w-full h-full lozad\" alt=\"Solving Simultaneous Equations By Substitution\" title=\"Solving Simultaneous Equations By Substitution\" onError=\"handleImageNotLoadedError(this)\" data-default-image=\"https://static.lp.lexp.cloud/images/attachment_defaults/resource/large/missing.png\" data-src=\"https://cdnapisec.kaltura.com/p/1776261/thumbnail/entry_id/1_e2unj66o/width/250/vid_slices/3/vid_slice/1\" width=\"315\" height=\"220\" src=\"data:image/png;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs\" /\u003e\n\u003cspan aria-hidden='true' class='flex justify-center items-center bg-white rounded-full w-16 h-16 absolute top-1/2 left-1/2 -mt-8 -ml-8 cursor-pointer z-0 border-2 border-primary drop-shadow-md lp-boclips-thumbnail-playBtn'\u003e\n\u003ci class='fa-solid fa-play text-primary text-3xl ml-1 drop-shadow-xl'\u003e\u003c/i\u003e\n\u003c/span\u003e\n\u003c/a\u003e\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n"}