Question

solve the system of equations.
$-9y + 4x - 11 = 0$
$-3y + 10x + 31 = 0$
$x = square$
$y = square$
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Explanation:

Step1: Rewrite equations clearly

Equation 1: $4x - 9y = 11$
Equation 2: $10x - 3y = -31$

Step2: Eliminate $y$: scale Eq2

Multiply Eq2 by 3: $30x - 9y = -93$

Step3: Subtract Eq1 from scaled Eq2

$(30x - 9y) - (4x - 9y) = -93 - 11$
$26x = -104$

Step4: Solve for $x$

$x = \frac{-104}{26} = -4$

Step5: Substitute $x=-4$ into Eq1

$4(-4) - 9y = 11$
$-16 - 9y = 11$

Step6: Solve for $y$

$-9y = 11 + 16 = 27$
$y = \frac{27}{-9} = -3$

Answer:

$x = -4$
$y = -3$