Question

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

−6x+y=32
(1 point)
(
,
)

Answer 1

To solve the system of equations:

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

Let's start by manipulating the first equation to express it in terms of \(y\):

From equation 1:
\[
4x - 8y = -36
\]
Divide the entire equation by 4:
\[
x - 2y = -9
\]
Now, solve for \(y\):
\[
-2y = -9 - x \\
y = \frac{9 + x}{2}
\]

Now substitute \(y\) in terms of \(x\) into equation 2:
\[
-6x + \left(\frac{9 + x}{2}\right) = 32
\]

To eliminate the fraction, multiply the entire equation by 2:
\[
-12x + 9 + x = 64
\]

Combine like terms:
\[
-11x + 9 = 64 \\
-11x = 64 - 9 \\
-11x = 55 \\
x = -5
\]

Now substitute the value of \(x\) back into our equation for \(y\):
\[
y = \frac{9 + (-5)}{2} \\
y = \frac{4}{2} \\
y = 2
\]

Thus, the solution to the system of equations is:
\[
\boxed{(-5, 2)}
\]