Question

how many solutions these pair of equations x-4y-6=0and 3x-4y-6=0 will have ​

Answer 1

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$\tt{x - 4y - 6 = 0 }\\ \tt{3x - 4y - 6 = 0}$

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$\blue{x = \frac{1}{2}} \\ \blue{ y = - 22}$

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$\tt{x - 4y = 6.......(i) }\\ \tt{3x - 4y = 6.....(ii)}$

$\tt{on \: subtracting\: equation \: (i) \: from \: (ii) \: we \: get}$

$\tt{3x - \cancel{4y} = \cancel{ 6}} \\ \tt{x - \cancel{4y} = \cancel{6} }\\ - \: \: \: \: \: \: \: \: \: + \: \: \: \: \: \: \: - \\ - - - - - - - - \\ \tt{ \to2x = 0 }\\ \tt {\red{ \to x = \frac{1}{2} }}$

$\tt{on \: putting \: x = \frac{1}{2} on \: equation \: (i) \: we \: get}$

$\tt{ \to \: x - 4y = 6 }\\ \tt{ \to \frac{1}{2} - 4y = 6 }\\ \tt{ \to\frac{1}{2} - 6 = 4y} \\ \tt{ \to\frac{1 - 12}{2} = 4y} \\ \tt{ \to4y = \frac{ - 11}{2}} \\ \tt{ \to y = \frac{ - 11}{ \cancel{ {2}}^{1} } \times \cancel {{4}}^{2} } \\ \tt{ \to \: \red { y = - 22}}$