Question

solve 2x+3y=11 and 2x-4y=-24 hence the find the of m for which y=mx+3

Answer 1

X=-1/2, y=4, and m=-2

Answer 2

Given pair of linear equation is:
$2x + 3y = 11 \\ 2x - 4y = - 24 \\ from \: 2 \\ 2x = 4y - 24 \\ 2x = 2(2y - 12) \\ \: \: x =2y - 12 \\ substitute \: the \: value \:of \: x \: in (1) \: we \: get \\ 2(2y - 12) + 3y = 11 \\ 4y - 24 + 3y = 11 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 7y =35 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: y = \frac{35}{7} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: y = 5 \\ substitute \: the \: value \: of \: y \: in \: (3)we \: get \\ \: \: \: \: \: \: x = 2(5) - 12 \\ \: \: \: \: \: \: x = 10 - 12 \\ \: \: \: \: \: \: x = - 2 \\ now \: consider \: y = mx + 3 \\ substitute \: the \: value \: of \: x and y \: weget \\ 5 = m( - 2) + 3 \\ 5 - 3 = - 2m \\ 2 = - 2m \\ - 2m = 2 \\ m = - 1 \: \\ hence \: x = - 2 \: y = 5 \: m = - 1$
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