`4x+3y=17`, `3x-4y+6=0`

Explanation

Given equations are `4 x+3 y=17` and `3 x-4 y+6=0`


Comparing with `{a}_{1} {x}+{b}_{1} {y}+{c}_{1}=0` and `{a}_{2} {x}+{b}_{2} {y}+{c}_{2}=0` we have `{a}_{1}=4, {~b}_{1}=3, {c}_{1}=-17` and `{a}_{2}=3, {~b}_{2}=-4, {c}_{2}=6`


Now,`x=\frac{b_{1} c_{2}-b_{2} c_{1}}{a_{1} b_{2}-a_{2} b_{1}}` and `y=\frac{c_{1} a_{2}-c_{2} a_{1}}{a_{1} b_{2}-a_{2} b_{1}}`


`\Rightarrow x=\frac{3 \times 6-(-4) \times(-17)}{4 x(-4)-3 \times 3}` and `y=\frac{-17 \times-6 \times 4}{4 \times(-4)-3 \times 3}`


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