{"id":2663,"date":"2023-05-04T10:00:48","date_gmt":"2023-05-04T04:30:48","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=2663"},"modified":"2023-05-05T09:15:57","modified_gmt":"2023-05-05T03:45:57","slug":"solution-of-linear-equation-two-variables","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/solution-of-linear-equation-two-variables\/","title":{"rendered":"Solution Of A Linear Equation In Two Variables"},"content":{"rendered":"<h2><strong>Solution Of A Linear Equation In Two Variables Example Problems With Solutions<\/strong><\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-12386\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/08\/Linear-Equation-In-Two-Variables.jpg\" alt=\"\" width=\"515\" height=\"368\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/08\/Linear-Equation-In-Two-Variables.jpg 515w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/08\/Linear-Equation-In-Two-Variables-300x214.jpg 300w\" sizes=\"(max-width: 515px) 100vw, 515px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-12385\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/08\/Linear-Equation-In-Two-Variables-1.jpg\" alt=\"\" width=\"668\" height=\"448\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/08\/Linear-Equation-In-Two-Variables-1.jpg 668w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/08\/Linear-Equation-In-Two-Variables-1-300x201.jpg 300w\" sizes=\"(max-width: 668px) 100vw, 668px\" \/><\/p>\n<p><strong>Method:<\/strong> Put the value of x (or y) = 0, \u00b11, \u00b12, \u00b13,\u2026\u2026, we get values of y (or x). By this we can find many solutions of given equation.<\/p>\n<p><strong>Read More:<\/strong><\/p>\n<ul>\n<li><span style=\"font-weight: 400;\"><a href=\"https:\/\/www.aplustopper.com\/what-is-a-linear-equation\/\">What is a Linear Equation<\/a><\/span><\/li>\n<li><a href=\"https:\/\/www.aplustopper.com\/linear-equations-in-one-variable\/\"><span style=\"font-weight: 400;\">Linear Equations In One Variable<\/span><\/a><\/li>\n<li><a href=\"https:\/\/www.aplustopper.com\/graphical-method\/\">Graphical Method Of Solving Linear Equations In Two Variables<\/a><\/li>\n<li><a href=\"https:\/\/www.aplustopper.com\/lesson\/rs-aggarwal-class-10-solutions-linear-equations-in-two-variables\/\"><span style=\"font-weight: 400;\">RS Aggarwal Class 10 Solutions Linear Equations In Two Variables<\/span><\/a><\/li>\n<li><a href=\"https:\/\/www.aplustopper.com\/lesson\/rs-aggarwal-class-9-solutions-linear-equations-in-two-variables\/\"><span style=\"font-weight: 400;\">RS Aggarwal Class 9 Solutions Linear Equations In Two Variables<\/span><\/a><\/li>\n<li><a href=\"https:\/\/www.aplustopper.com\/linear-equations-rs-aggarwal-class-8-maths-solutions-ex-8a\/\"><span style=\"font-weight: 400;\">RS Aggarwal Class 8 Solutions Linear Equations<\/span><\/a><\/li>\n<li><a href=\"https:\/\/www.aplustopper.com\/linear-equation-one-variable-rs-aggarwal-class-7-solutions\/\"><span style=\"font-weight: 400;\">RS Aggarwal Class 7 Solutions Linear Equations in One Variable<\/span><\/a><\/li>\n<li><span style=\"font-weight: 400;\"><a href=\"https:\/\/www.aplustopper.com\/linear-equation-one-variable-rs-aggarwal-class-6-maths-solutions-ex-9a\/\">RS Aggarwal Class 6 Solutions Linear Equation In One Variable<\/a><\/span><\/li>\n<\/ul>\n<p><iframe loading=\"lazy\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/DWj-aRuMaJU?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<p><strong>Example 1:<\/strong> \u00a0 \u00a0Find five solutions of<br \/>\n(i) 2x + 3y = 6 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(ii) 3x \u2013 2y = 12 \u00a0 \u00a0 \u00a0 \u00a0\u00a0(iii) 7x + y = 15<br \/>\n<strong>Solution: \u00a0 \u00a0<\/strong>(i) 2x = 6 \u2013 3y<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-135402\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/04\/Solution-Of-A-Linear-Equation-In-Two-Variables-1.png\" alt=\"Solution Of A Linear Equation In Two Variables 1\" width=\"332\" height=\"493\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/04\/Solution-Of-A-Linear-Equation-In-Two-Variables-1.png 332w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/04\/Solution-Of-A-Linear-Equation-In-Two-Variables-1-202x300.png 202w\" sizes=\"(max-width: 332px) 100vw, 332px\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-135403\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/04\/Solution-Of-A-Linear-Equation-In-Two-Variables-2.png\" alt=\"Solution Of A Linear Equation In Two Variables 2\" width=\"402\" height=\"377\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/04\/Solution-Of-A-Linear-Equation-In-Two-Variables-2.png 402w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/04\/Solution-Of-A-Linear-Equation-In-Two-Variables-2-300x281.png 300w\" sizes=\"(max-width: 402px) 100vw, 402px\" \/><\/p>\n<p><strong>Example 2:<\/strong>\u00a0 \u00a0\u00a0Find two solutions of<br \/>\n(i) 3x \u2013 7y = 21 (ii) 8x \u2013 5y = 16<br \/>\n<strong>Solution: \u00a0 \u00a0<\/strong>(i) 3x \u2013 7y = 21<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-135405\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/04\/Solution-Of-A-Linear-Equation-In-Two-Variables-3.png\" alt=\"Solution Of A Linear Equation In Two Variables 3\" width=\"300\" height=\"226\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-135406\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/04\/Solution-Of-A-Linear-Equation-In-Two-Variables-4.png\" alt=\"Solution Of A Linear Equation In Two Variables 4\" width=\"304\" height=\"549\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/04\/Solution-Of-A-Linear-Equation-In-Two-Variables-4.png 304w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/04\/Solution-Of-A-Linear-Equation-In-Two-Variables-4-166x300.png 166w\" sizes=\"(max-width: 304px) 100vw, 304px\" \/><\/p>\n<p><iframe loading=\"lazy\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/JQCFvzXa8Bo?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<p><strong>Example 3:<\/strong>\u00a0 \u00a0 Find five solutions of<br \/>\n(i) 3x = 5 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (ii) 7y = 10<br \/>\n<strong>Solution: \u00a0 \u00a0<\/strong>(i) The equation is only in one variable. So we have to convert into 2 variable 3x + 0.y = 5<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-135407\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/04\/Solution-Of-A-Linear-Equation-In-Two-Variables-5.png\" alt=\"Solution Of A Linear Equation In Two Variables 5\" width=\"390\" height=\"381\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/04\/Solution-Of-A-Linear-Equation-In-Two-Variables-5.png 390w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/04\/Solution-Of-A-Linear-Equation-In-Two-Variables-5-300x293.png 300w\" sizes=\"(max-width: 390px) 100vw, 390px\" \/><br \/>\n<strong>Note:<\/strong><br \/>\n<strong>Ordered Pair:<\/strong> If value of x &amp; y are represent in form (x, y) then this form is called ordered pair form : Eg. x = 5, y = 7\/3 then ordered pair form = (5, 7\/3). First part is called abscissa (x part) and second part is ordinate (y part).<\/p>\n<p><strong>Example 4: \u00a0<\/strong> \u00a0Check the following value of x &amp; y are solution of equation 9x \u2013 8y = 72 or not<br \/>\n(i) (0, 9) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (ii) (0, \u2013 9) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (iii) (\u2013 8, 0)<br \/>\n(iv) (+8, 0) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (v) (1, 1) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(vi) (1\/3, 1\/2)<br \/>\n<strong>Solution: \u00a0 \u00a0<\/strong>Given equation 9x \u2013 8y = 72<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-135408\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/04\/Solution-Of-A-Linear-Equation-In-Two-Variables-6.png\" alt=\"Solution Of A Linear Equation In Two Variables 6\" width=\"370\" height=\"547\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/04\/Solution-Of-A-Linear-Equation-In-Two-Variables-6.png 370w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/04\/Solution-Of-A-Linear-Equation-In-Two-Variables-6-203x300.png 203w\" sizes=\"(max-width: 370px) 100vw, 370px\" \/><\/p>\n<p><strong>Example 5: \u00a0 \u00a0<\/strong>Find the value of k in equation 2x + ky = 6 if (\u20132, 2) is a solution.<br \/>\n<strong>Solution: \u00a0 \u00a0<\/strong>\u2235 (\u20132, 2) is a solution of 2x + ky = 5<br \/>\n\u2234 2(\u20132) + k(2) = 6<br \/>\n\u2013 4 + 2k = 6 \u21d2 2k = 6 + 4<br \/>\nk = 10\/2 = 5<\/p>\n<p><strong>Example 6: \u00a0 \u00a0<\/strong>Find value of p if (4, \u20134) is a solution of x \u2013 py = 8.<br \/>\n<strong>Solution: \u00a0 \u00a0<\/strong>x \u2013 py = 8<br \/>\n4 \u2013 p (\u20134) = 8<br \/>\n4p = 8 \u2013 4<br \/>\n4p = 4<br \/>\np = 1<\/p>\n<p><strong>Example 7: \u00a0<\/strong> \u00a0Find the value of a if (a, \u20133a) is a solution of 14x + 3y = 35.<br \/>\n<strong>Solution: \u00a0 \u00a0<\/strong>Put x = a and y = \u20133a in given equation<br \/>\n14(a) + 3(\u20133a) = 35<br \/>\n14a \u2013 9a = 35<br \/>\n5a = 35<br \/>\na = 7<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution Of A Linear Equation In Two Variables Example Problems With Solutions Method: Put the value of x (or y) = 0, \u00b11, \u00b12, \u00b13,\u2026\u2026, we get values of y (or x). By this we can find many solutions of given equation. Read More: What is a Linear Equation Linear Equations In One Variable Graphical [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[5],"tags":[1133,52,1143,1144],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.8 (Yoast SEO v17.8) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Solution Of A Linear Equation In Two Variables - A Plus Topper<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.aplustopper.com\/solution-of-linear-equation-two-variables\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Solution Of A Linear Equation In Two Variables\" \/>\n<meta property=\"og:description\" content=\"Solution Of A Linear Equation In Two Variables Example Problems With Solutions Method: Put the value of x (or y) = 0, \u00b11, \u00b12, \u00b13,\u2026\u2026, we get values of y (or x). By this we can find many solutions of given equation. 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By this we can find many solutions of given equation. 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