{"id":10910,"date":"2022-06-07T15:41:50","date_gmt":"2022-06-07T10:11:50","guid":{"rendered":"https:\/\/mathemerize.com\/?p=10910"},"modified":"2022-06-07T15:48:27","modified_gmt":"2022-06-07T10:18:27","slug":"which-of-the-following-pairs-of-linear-equations-are-consistent-obtain-the-solution-in-such-cases-graphically","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/which-of-the-following-pairs-of-linear-equations-are-consistent-obtain-the-solution-in-such-cases-graphically\/","title":{"rendered":"Which of the following pairs of linear equations are consistent obtain the solution in such cases graphically."},"content":{"rendered":"\n

Question<\/strong> : Which of the following pairs of linear equations are consistent obtain the solution in such cases graphically.<\/p>\n\n\n\n

(i)<\/strong> x + y = 5, 2x + 2y = 10<\/p>\n\n\n\n

(ii) <\/strong> x – y = 8, 3x – 3y = 10<\/p>\n\n\n\n

(iii)<\/strong> 2x + y – 6 = 0, 4x – 2y – 4 = 0<\/p>\n\n\n\n

(iv)<\/strong> 2x – 2y – 2 = 0, 4x – 4y – 5 = 0<\/p>\n\n\n\n

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

(i)<\/strong> We have the given equations,<\/p>\n\n\n\n

x + y = 5 \\(\\implies\\) y = 5 – x<\/p>\n\n\n\n

If x = 0, y = 5<\/p>\n\n\n\n

If x = 5, y = 0<\/p>\n\n\n\n

x<\/td>0<\/td>5<\/td><\/tr>
y = 5 – x<\/td>5<\/td>0<\/td><\/tr>
Points<\/td>A<\/td>B<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

and 2x + 2y = 10 \\(\\implies\\) y = \\(10 – 2x\\over 2\\)<\/p>\n\n\n\n

If x = 0, y = 5<\/p>\n\n\n\n

If x = 2, y = 3<\/p>\n\n\n\n

If x = 5, y = 0<\/p>\n\n\n\n

x<\/td>0<\/td>2<\/td>5<\/td><\/tr>
y = \\(10 – 2x\\over 2\\)<\/td>5<\/td>3<\/td>0<\/td><\/tr>
Points<\/td>C<\/td>D<\/td>E<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Now, plot these points in the table on graph as shown in figure below. By plotting A and B points we get the line AB and by plotting C, D and E points we get the line CD.<\/p>\n\n\n\n

We see that both the lines in the graph are coincident. Therefore both equations have infinitely many solutions.<\/strong><\/p>\n\n\n\n

Hence, the pair of linear equations is consistent.<\/strong><\/p>\n\n\n\n

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

(ii)<\/strong> We have the given equations,<\/p>\n\n\n\n

x – y = 8 \\(\\implies\\) y = x – 8<\/p>\n\n\n\n

If x = 0, y = -8<\/p>\n\n\n\n

If x = 8, y = 0<\/p>\n\n\n\n

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

and 3x – 3y = 16 \\(\\implies\\) y = \\(3x – 16\\over 3\\)<\/p>\n\n\n\n

If x = 0, y = \\(-16\\over 3\\)<\/p>\n\n\n\n

If x = 2, y = \\(-10\\over 3\\)<\/p>\n\n\n\n

x<\/td>0<\/td>2<\/td><\/tr>
y = \\(3x – 16\\over 3\\)<\/td>\\(-16\\over 3\\)<\/td>\\(-10\\over 3\\)<\/td><\/tr>
Points<\/td>C<\/td>D<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Now, plot these points in the table on graph as shown in figure below. By plotting A and B points we get the line AB and by plotting C and D points we get the line CD.<\/p>\n\n\n\n

We see that both the lines are parallel. Therefore both equations have has no solution.<\/strong><\/p>\n\n\n\n

Hence, the pair of linear equations is inconsistent.<\/strong><\/p>\n\n\n\n

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

(iii)<\/strong> We have the given equations,<\/p>\n\n\n\n

2x + y – 6 = 0 \\(\\implies\\) y = 6 – 2x<\/p>\n\n\n\n

If x = 0, y = 6<\/p>\n\n\n\n

If x = 3, y = 0<\/p>\n\n\n\n

x<\/td>0<\/td>3<\/td><\/tr>
y<\/td>6<\/td>0<\/td><\/tr>
Points<\/td>A<\/td>B<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

and 4x – 2y – 4 = 0 \\(\\implies\\) y = 2x – 2<\/p>\n\n\n\n

If x = 0, y = 1<\/p>\n\n\n\n

If x = -2, y = 0<\/p>\n\n\n\n

x<\/td>0<\/td>1<\/td><\/tr>
y<\/td>-2<\/td>0<\/td><\/tr>
Point<\/td>D<\/td>E<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Now, plot these points in the table on graph as shown in figure below. By plotting A and B points we get the straight line AB and by plotting C, D points we get the line CD.<\/p>\n\n\n\n

The lines AB and CD intersect at E.<\/p>\n\n\n\n

We see that both the lines in the graph have a common point E. Therefore the given equations is consistent and this point E gives us the solution of both the lines.<\/strong><\/p>\n\n\n\n

Hence, the pair of linear equations is consistent.<\/strong><\/p>\n\n\n\n

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

(iv)<\/strong> We have the given equations,<\/p>\n\n\n\n

2x – 2y – 2 = 0 \\(\\implies\\) y = x – 1<\/p>\n\n\n\n

If x = 0, y = -1<\/p>\n\n\n\n

If x = 1, y = 0<\/p>\n\n\n\n

x<\/td>0<\/td>1<\/td><\/tr>
y<\/td>-1<\/td>0<\/td><\/tr>
Points<\/td>A<\/td>B<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

and 4x – 4y – 5 = 0 \\(\\implies\\) y = \\(x – {5\\over 4}\\)<\/p>\n\n\n\n

If x = 0, y = \\(-5\\over 4\\)<\/p>\n\n\n\n

If x = \\(5\\over 4\\), y = 0<\/p>\n\n\n\n

x<\/td>0<\/td>\\(-5\\over 4\\)<\/td><\/tr>
y<\/td>\\(5\\over 4\\)<\/td>0<\/td><\/tr>
Points<\/td>C<\/td>D<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Now, plot these points in the table on graph as shown in figure below. By plotting A and B points we get the line AB and by plotting C and D points we get the line CD.<\/p>\n\n\n\n

We see that both the lines are parallel. Therefore both equations have has no solution.<\/strong><\/p>\n\n\n\n

Hence, the pair of linear equations is inconsistent.<\/strong><\/p>\n\n\n\n

\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

Question : Which of the following pairs of linear equations are consistent obtain the solution in such cases graphically. (i) x + y = 5, 2x + 2y = 10 (ii) x – y = 8, 3x – 3y = 10 (iii) 2x + y – 6 = 0, 4x – 2y – 4 = …<\/p>\n

Which of the following pairs of linear equations are consistent obtain the solution in such cases 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":"\nWhich of the following pairs of linear equations are consistent obtain the solution in such cases 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\/which-of-the-following-pairs-of-linear-equations-are-consistent-obtain-the-solution-in-such-cases-graphically\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Which of the following pairs of linear equations are consistent obtain the solution in such cases graphically. - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Question : Which of the following pairs of linear equations are consistent obtain the solution in such cases graphically. 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