Question

find the solution of the system of equations.
$3x + 2y = -16$
$-3x - 8y = 46$
answer attempt 1 out of 2
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Explanation:

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

We have the system:
\[

$$\begin{cases} 3x + 2y = -16 \\ -3x - 8y = 46 \end{cases}$$

\]
Adding the left - hand sides and the right - hand sides of the two equations:
\((3x + 2y)+(-3x - 8y)=-16 + 46\)
Simplify the left - hand side: \(3x-3x+2y - 8y=-6y\)
Simplify the right - hand side: \(30\)
So we get the equation \(-6y = 30\)

Step2: Solve for \(y\)

From \(-6y=30\), divide both sides by \(-6\):
\(y=\frac{30}{-6}=-5\)

Step3: Substitute \(y = - 5\) into one of the original equations to solve for \(x\)

Substitute \(y=-5\) into the first equation \(3x + 2y=-16\):
\(3x+2\times(-5)=-16\)
Simplify: \(3x-10=-16\)
Add \(10\) to both sides: \(3x=-16 + 10=-6\)
Divide both sides by \(3\): \(x=\frac{-6}{3}=-2\)

Answer:

\((-2,-5)\)