{"id":10946,"date":"2022-06-09T14:56:44","date_gmt":"2022-06-09T09:26:44","guid":{"rendered":"https:\/\/mathemerize.com\/?p=10946"},"modified":"2022-06-09T14:56:48","modified_gmt":"2022-06-09T09:26:48","slug":"given-the-linear-equation-2x-3y-8-0-write-another-linear-equation-in-two-variables-such-that-the-geometrical-representation-of-the-pair-so-formed-is","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/given-the-linear-equation-2x-3y-8-0-write-another-linear-equation-in-two-variables-such-that-the-geometrical-representation-of-the-pair-so-formed-is\/","title":{"rendered":"Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is :"},"content":{"rendered":"\n
Question<\/strong> : Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is :<\/p>\n\n\n\n (i) <\/strong> intersecting lines<\/p>\n\n\n\n (ii)<\/strong> parallel lines<\/p>\n\n\n\n (iii)<\/strong> coincident lines<\/p>\n\n\n\n Solution<\/strong> : The given linear equation is 2x + 3y – 8 = 0<\/p>\n\n\n\n (i) <\/strong> For intersecting lines, we know that<\/p>\n\n\n\n \\(a_1\\over a_2\\) \\(\\ne\\) \\(b_1\\over b_2\\)<\/p>\n\n\n\n Any intersecting line may be taken as<\/p>\n\n\n\n 5x + 2y – 9 = 0<\/strong><\/p>\n\n\n\n (ii)<\/strong> For parallel lines, \\(a_1\\over a_2\\) = \\(b_1\\over b_2\\) \\(\\ne\\) \\(c_1\\over c_2\\)<\/p>\n\n\n\n \\(\\therefore\\) line parallel to 2x + 3y – 8 = 0 may be taken as<\/p>\n\n\n\n 6x + 9y + 7 = 0<\/strong><\/p>\n\n\n\n (iii)<\/strong> For coincident lines, \\(a_1\\over a_2\\) = \\(b_1\\over b_2\\) = \\(c_1\\over c_2\\)<\/p>\n\n\n\n Any line coincident to 2x + 3y – 8 = 0 may be taken as<\/p>\n\n\n\n 4x + 3y – 16 = 0<\/strong><\/p>\n\n\n\n <\/p>\n","protected":false},"excerpt":{"rendered":" Question : Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is : (i) intersecting lines (ii) parallel lines (iii) coincident lines Solution : The given linear equation is 2x + 3y – 8 = 0 …<\/p>\n