Question

Systems of Linear Equations Unit Test
7 of 147 of 14 Items














Question
Solve the system of equations.
4x−8y=−36

−6x+y=32

Answer 1

To solve the system of equations:

1. \(4x - 8y = -36\) (Equation 1)
2. \(-6x + y = 32\) (Equation 2)

We can use the substitution or elimination method. Here, we'll use the elimination method.

First, let's manipulate the equations to make it easier to eliminate one variable.

From Equation 2, we can express \(y\) in terms of \(x\):
\[
y = 6x + 32
\]

Next, we can substitute this expression for \(y\) in Equation 1:
\[
4x - 8(6x + 32) = -36
\]

Now, simplify and solve for \(x\):
\[
4x - 48x - 256 = -36
\]
\[
-44x - 256 = -36
\]
\[
-44x = -36 + 256
\]
\[
-44x = 220
\]
\[
x = \frac{220}{-44}
\]
\[
x = -5
\]

Now, substitute \(x = -5\) back into the expression we found for \(y\):
\[
y = 6(-5) + 32
\]
\[
y = -30 + 32
\]
\[
y = 2
\]

So the solution to the system of equations is:
\[
(x, y) = (-5, 2)
\]

Thus, the answer is:
\[
\boxed{(-5, 2)}
\]