{"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":"
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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