Question

find the solution of the system of equations.

$-5x + 9y = -32$
$-5x - 3y = 4$

answer attempt 1 out of 2

$(square, square)$ submit answer

Explanation:

Step1: Subtract the two equations to eliminate \(x\)

We have the system:

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Subtract equation \((2)\) from equation \((1)\):

$$ (-5x + 9y) - (-5x - 3y) = -32 - 4 $$

Simplify the left side: \(-5x + 9y + 5x + 3y = 12y\)
Simplify the right side: \(-36\)
So we get \(12y = -36\)

Step2: Solve for \(y\)

Divide both sides of \(12y = -36\) by \(12\):

$$ y = \frac{-36}{12} = -3 $$

Step3: Substitute \(y = -3\) into one of the original equations to solve for \(x\)

Let's use equation \((2)\): \(-5x - 3y = 4\)
Substitute \(y = -3\):

$$ -5x - 3(-3) = 4 $$

Simplify: \(-5x + 9 = 4\)
Subtract \(9\) from both sides: \(-5x = 4 - 9 = -5\)
Divide both sides by \(-5\): \(x = \frac{-5}{-5} = 1\)

Answer:

\((1, -3)\)