{"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 For equation y = x + 4,<\/p>\n\n\n\n Now plot these points on graph :<\/p>\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 For equation 7x + 5y = 46,<\/p>\n\n\n\n Now plot these points on graph :<\/p>\n\n\n\nx<\/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 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 x<\/td> 10<\/td> 3<\/td><\/tr> y<\/td> 0<\/td> 5<\/td><\/tr><\/tbody><\/table><\/figure>\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