Question

solve the following system of equations.
6x - 5y = 18
-5x + 6y = -15
x =

y =

Explanation:

Step1: Eliminate x, scale equations

Multiply first eq by 5: $30x - 25y = 90$
Multiply second eq by 6: $-30x + 36y = -90$

Step2: Add scaled equations

$(30x -25y) + (-30x +36y) = 90 + (-90)$
$11y = 0$

Step3: Solve for y

$y = \frac{0}{11} = 0$

Step4: Substitute y=0 into first eq

$6x - 5(0) = 18$
$6x = 18$

Step5: Solve for x

$x = \frac{18}{6} = 3$

Answer:

$x = 3$
$y = 0$