Question

Solve the system of equations.
−6x+2y=−32

4x+3y=−9
(1 point)

Answer 1

To solve the system of equations:

1. \(-6x + 2y = -32\)
2. \(4x + 3y = -9\)

We can use the substitution or elimination method. Let's use the elimination method.

First, let's rearrange equation 1 to solve for \(y\).

\[-6x + 2y = -32\]

Add \(6x\) to both sides:

\[2y = 6x - 32\]

Now, divide everything by 2:

\[y = 3x - 16\] (Equation 3)

Now, we can substitute equation 3 into equation 2:

\[4x + 3(3x - 16) = -9\]

Distributing \(3\):

\[4x + 9x - 48 = -9\]

Combine like terms:

\[13x - 48 = -9\]

Add \(48\) to both sides:

\[13x = 39\]

Now, divide by \(13\):

\[x = 3\]

Now, substitute \(x = 3\) back into equation 3 to find \(y\):

\[y = 3(3) - 16\]

\[y = 9 - 16\]

\[y = -7\]

So, the solution to the system of equations is:

\((x, y) = (3, -7)\)

To verify, we can plug these values back into the original equations:

1. For \(-6(3) + 2(-7) = -32\):

\(-18 - 14 = -32\) → True

2. For \(4(3) + 3(-7) = -9\):

\(12 - 21 = -9\) → True

Both equations are satisfied, so the solution is correct.

**Final Answer:** \( (x, y) = (3, -7) \)