Question

3x + 4y =16 ;4x - 3y =6 elimination method

Answer 1

$\binom{3x + 4y = 16}{4x - 3y = 6} \\ \\ multiply \: both \: of \: the \: sides \: of \\ \: 3x + 4y = 16 \: by \: 3 \\ \\ \binom{9x + 12y = 48}{4x - 3y = 6} \\ \\ multiply \: both \: sides \: of \\ \: 4x - 3y = 6 \: by \: 4 \\ \\ \binom{9x + 12y = 48}{16x - 12y = 24} \\ \\ sum \: the \: equation \: vertically \: \\ \\ 9x + 12y + 16x - 12y = 48 + 24$

$25x = 72 \\ \\ x = \frac{72}{25} \\ \\ substitute \: the \: value \: of \: x \: in \: 4x - 3y = 6 \\ \\ 4 \times \frac{72}{25} - 3y = 6 \\ \\ \frac{288}{25} - 3y = 6 \\ \\ - 3y = 6 - \frac{288}{25} \\ \\ - 3y = - \frac{138}{25} \\ \\ y = \frac{46}{25} \\ \\ therefore \: \\ \\ x = \frac{72}{25} \: and \: y = \frac{46}{25}$