{"id":10885,"date":"2022-06-05T17:04:33","date_gmt":"2022-06-05T11:34:33","guid":{"rendered":"https:\/\/mathemerize.com\/?p=10885"},"modified":"2022-06-05T17:04:36","modified_gmt":"2022-06-05T11:34:36","slug":"on-comparing-the-ratios-a_1over-a_2-b_1over-b_2-and-c_1over-c_2-find-out-whether-the-lines-representing-the-following-pair-of-linear-equations-intersect-at-a-point-are-paral","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/on-comparing-the-ratios-a_1over-a_2-b_1over-b_2-and-c_1over-c_2-find-out-whether-the-lines-representing-the-following-pair-of-linear-equations-intersect-at-a-point-are-paral\/","title":{"rendered":"On comparing the ratios \\(a_1\\over a_2\\), \\(b_1\\over b_2\\) and \\(c_1\\over c_2\\), find out whether the lines representing the following pair of linear equations intersect at a point, are parallel of coincide."},"content":{"rendered":"

<\/p>\n

Question<\/strong> : On comparing the ratios \\(a_1\\over a_2\\), \\(b_1\\over b_2\\) and \\(c_1\\over c_2\\), find out whether the lines representing the following pair of linear equations intersect at a point, are parallel of coincide.<\/p>\n

<\/p>\n

(i)<\/strong> 5x – 4y + 8 = 0; 7x + 6y – 9 = 0<\/p>\n

<\/p>\n

(ii)<\/strong> 9x + 3y + 12 = 0; 18x + 6y + 24 = 0<\/p>\n

<\/p>\n

(iii)<\/strong> 6x – 3y + 10 = 0; 2x – y + 9 = 0<\/p>\n

<\/p>\n

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

(i)\u00a0\u00a0<\/strong>Linear Equations given are<\/p>\n

5x – 4y + 8 = 0<\/p>\n

and\u00a0 7x + 6y – 9 = 0<\/p>\n

Here, \\(a_1\\over a_2\\) \\(\\ne\\) \\(b_1\\over b_2\\)<\/p>\n

i.e.\u00a0 \\(5\\over 7\\) \\(\\ne\\) \\(-4\\over 6\\)<\/p>\n

So, given lines are intersecting lines.<\/strong><\/p>\n

<\/p>\n

(ii)\u00a0\u00a0<\/strong>Linear Equations given are<\/p>\n

9x + 3y + 12 = 0<\/p>\n

and\u00a0 18x + 6y + 24 = 0<\/p>\n

Here, \\(a_1\\over a_2\\) = \\(b_1\\over b_2\\) = \\(c_1\\over c_2\\)<\/p>\n

i.e.\u00a0 \\(9\\over 18\\) = \\(3\\over 6\\) = \\(12\\over 24\\)<\/p>\n

So, given lines are coincident lines.<\/strong><\/p>\n

<\/p>\n

(iii)\u00a0\u00a0<\/strong>Linear Equations given are<\/p>\n

6x – 3y + 10 = 0<\/p>\n

and\u00a0 2x – y + 9 = 0<\/p>\n

Here, \\(a_1\\over a_2\\) = \\(b_1\\over b_2\\) \\(\\ne\\) \\(c_1\\over c_2\\)<\/p>\n

i.e.\u00a0 \\(6\\over 2\\) = \\(-3\\over -1\\) \\(\\ne\\) \\(10\\over 9\\)<\/p>\n

So, given lines are parallel lines.<\/strong><\/p>\n

<\/p>\n\n\n

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

Question : On comparing the ratios \\(a_1\\over a_2\\), \\(b_1\\over b_2\\) and \\(c_1\\over c_2\\), find out whether the lines representing the following pair of linear equations intersect at a point, are parallel of coincide. (i) 5x – 4y + 8 = 0; 7x + 6y – 9 = 0 (ii) 9x + 3y + 12 = …<\/p>\n

On comparing the ratios \\(a_1\\over a_2\\), \\(b_1\\over b_2\\) and \\(c_1\\over c_2\\), find out whether the lines representing the following pair of linear equations intersect at a point, are parallel of coincide.<\/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":"\nOn comparing the ratios \\(a_1\\over a_2\\), \\(b_1\\over b_2\\) and \\(c_1\\over c_2\\), find out whether the lines representing the following pair of linear equations intersect at a point, are parallel of coincide. - 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\/on-comparing-the-ratios-a_1over-a_2-b_1over-b_2-and-c_1over-c_2-find-out-whether-the-lines-representing-the-following-pair-of-linear-equations-intersect-at-a-point-are-paral\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"On comparing the ratios \\(a_1\\over a_2\\), \\(b_1\\over b_2\\) and \\(c_1\\over c_2\\), find out whether the lines representing the following pair of linear equations intersect at a point, are parallel of coincide. - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Question : On comparing the ratios (a_1over a_2), (b_1over b_2) and (c_1over c_2), find out whether the lines representing the following pair of linear equations intersect at a point, are parallel of coincide. 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