Question

Solve the system.
−5x+4y=48

−5x−8y=24
(1 point)
Responses

(8, 2)
left parenthesis 8 comma 2 right parenthesis

(−24,−18)
left parenthesis negative 24 comma negative 18 right parenthesis

(−8, 2)
left parenthesis negative 8 comma 2 right parenthesis

(24,−18)

Answer 1

To solve the system of equations:

1. \( -5x + 4y = 48 \) (Equation 1)
2. \( -5x - 8y = 24 \) (Equation 2)

We can use the elimination method.

First, let's write the two equations down again:

1. \( -5x + 4y = 48 \) (Eq. 1)
2. \( -5x - 8y = 24 \) (Eq. 2)

Next, subtract Eq. 2 from Eq. 1 to eliminate \( -5x \):

\[
(-5x + 4y) - (-5x - 8y) = 48 - 24
\]

This simplifies to:

\[
4y + 8y = 48 - 24
\]

\[
12y = 24
\]

Now, solve for \( y \):

\[
y = \frac{24}{12} = 2
\]

Now that we have \( y = 2 \), substitute \( y \) back into one of the original equations to find \( x \). We'll use Eq. 1:

\[
-5x + 4(2) = 48
\]

This simplifies to:

\[
-5x + 8 = 48
\]

Subtract 8 from both sides:

\[
-5x = 48 - 8
\]

\[
-5x = 40
\]

Now, divide by -5:

\[
x = \frac{40}{-5} = -8
\]

So the solution to the system of equations is:

\[
(x, y) = (-8, 2)
\]

Thus, the answer is **\( \mathbf{(-8, 2)} \)**.