Question

Solve for the value of $x$ and $y$: $31x-42y=51$ and $42x-31y=95$

Answer 1

Let $31x-42y=51$...(i) and $42x-31y=95$...(ii)

On adding (i) and (ii), we get,

$\Rightarrow 31x-42y+42x-31y=51+95$

$\Rightarrow 73x-73y=146$

$\Rightarrow x-y=2$ ...(iii)

On subtracting (i) from (ii), we get,

$\Rightarrow 42x-31y-31x+42y=95-51$

$\Rightarrow 11x+11y=44$

$\Rightarrow x+y=4$...(iv)

Now, adding (iii) ad (iv), we get,

$\Rightarrow x-y+x+y=2+4$

$\Rightarrow 2x=6$

$\Rightarrow x=3$

Therefore,

$\Rightarrow y=4-x=4-3=1$ [From (iv)]

Hence, $x=3$ and $y=1$