Question

9x + 7y = 2\
2x + 8y = -6

Explanation:

Step1: Eliminate x via scaling equations

Multiply first eq by 2: $18x + 14y = 4$
Multiply second eq by 9: $18x + 72y = -54$

Step2: Subtract scaled equations

Subtract first scaled eq from second:
$(18x + 72y) - (18x + 14y) = -54 - 4$
$58y = -58$

Step3: Solve for y

Divide both sides by 58:
$y = \frac{-58}{58} = -1$

Step4: Substitute y into second original eq

$2x + 8(-1) = -6$
$2x - 8 = -6$

Step5: Solve for x

Add 8 to both sides: $2x = 2$
Divide by 2: $x = \frac{2}{2} = 1$

Answer:

$x = 1$, $y = -1$