{"id":10871,"date":"2022-06-04T18:55:13","date_gmt":"2022-06-04T13:25:13","guid":{"rendered":"https:\/\/mathemerize.com\/?p=10871"},"modified":"2022-06-04T18:55:16","modified_gmt":"2022-06-04T13:25:16","slug":"from-the-pair-of-linear-equations-in-the-following-problems-and-find-their-solution-graphically","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/from-the-pair-of-linear-equations-in-the-following-problems-and-find-their-solution-graphically\/","title":{"rendered":"From the pair of linear equations in the following problems, and find their solution graphically."},"content":{"rendered":"\n

Question<\/strong> : From the pair of linear equations in the following problems, and find their solution graphically.<\/p>\n\n\n\n

(i) <\/strong> 10 students of class X took part in a mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.<\/p>\n\n\n\n

(ii)<\/strong> 5 pencils and 7 pens together cost Rs 50, whereas 7 pencils and 5 pens together cost Rs 46. Find the cost of one pencil and that of one pen.<\/p>\n\n\n\n

Solution<\/strong> :<\/p>\n\n\n\n

(i)<\/strong> Let x be the number of boys and y be the number of girls.<\/p>\n\n\n\n

Then the equations will be<\/p>\n\n\n\n

x + y = 10 …….(1)<\/p>\n\n\n\n

y = x + 4 …….(2)<\/p>\n\n\n\n

Let us now draw the graph of the above two equations by finding the solutions of equations.<\/p>\n\n\n\n

For equation x + y = 10<\/p>\n\n\n\n

x<\/td>0<\/td>8<\/td><\/tr>
y = 10 – x<\/td>10<\/td>2<\/td><\/tr>
Points<\/td>A<\/td>B<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

For equation y = x + 4,<\/p>\n\n\n\n

x<\/td>0<\/td>1<\/td>3<\/td><\/tr>
y = x + 4<\/td>4<\/td>5<\/td>7<\/td><\/tr>
Points<\/td>C<\/td>D<\/td>E<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Now plot these points on graph :<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The two lines AB and CE shown in the graph intersect at point E(3, 7). So, x = 3 and y = 7 is the required solution of the pair of linear equations.<\/p>\n\n\n\n

i.e. Number of Boys = 3, Number of girls = 7<\/strong><\/p>\n\n\n\n

(ii)<\/strong> Let x be the cost of one pencil and y be the cost of one pen. Then the equation formed will be <\/p>\n\n\n\n

5x + 7y = 50<\/p>\n\n\n\n

and 7x + 5y = 46<\/p>\n\n\n\n

Let us now draw the graph of the above two equations by finding the solutions of equations.<\/p>\n\n\n\n

For equation 5x + 7y = 50,<\/p>\n\n\n\n

x<\/td>10<\/td>3<\/td><\/tr>
y<\/td>0<\/td>5<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

For equation 7x + 5y = 46,<\/p>\n\n\n\n

x<\/td>8<\/td>3<\/td><\/tr>
y<\/td>-2<\/td>5<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Now plot these points on graph :<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The two lines as shown in the graph intersect at point (3, 5). So, x = 3 and y = 5<\/strong> is the required solution of the pair of linear equations.<\/p>\n","protected":false},"excerpt":{"rendered":"

Question : From the pair of linear equations in the following problems, and find their solution graphically. (i) 10 students of class X took part in a mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz. …<\/p>\n

From the pair of linear equations in the following problems, and find their solution graphically.<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[911,43],"tags":[],"yoast_head":"\nFrom the pair of linear equations in the following problems, and find their solution graphically. - Mathemerize<\/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:\/\/mathemerize.com\/from-the-pair-of-linear-equations-in-the-following-problems-and-find-their-solution-graphically\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"From the pair of linear equations in the following problems, and find their solution graphically. - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Question : From the pair of linear equations in the following problems, and find their solution graphically. 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