Question

solve the system of equation using elimination: -6x + 6y = 0; 9x - 8y = 4

Explanation:

Step1: Eliminate x, scale equations

Multiply first equation by 3: $-18x + 18y = 0$
Multiply second equation by 2: $18x - 16y = 8$

Step2: Add scaled equations

$(-18x + 18y) + (18x - 16y) = 0 + 8$
Simplify: $2y = 8$

Step3: Solve for y

$y = \frac{8}{2} = 4$

Step4: Substitute y into first equation

$-6x + 6(4) = 0$
Simplify: $-6x + 24 = 0$

Step5: Solve for x

$-6x = -24$
$x = \frac{-24}{-6} = 4$

Answer:

$x=4$, $y=4$