Question

Systems of Linear Equations Online Practice
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Question
Solve the system.
−5x+4y=48

−5x−8y=24
(1 point)
Responses

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

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

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

(−8, 2)

Answer 1

To solve the system of equations:

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

We can use substitution or elimination. Here, I'll use elimination.

First, we can eliminate \( -5x \) from both equations.

We can do this by subtracting the first equation from the second:

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

This simplifies to:

\[
-8y - 4y = -24
\]
\[
-12y = -24
\]
\[
y = 2
\]

Now that we have \( y = 2 \), we can substitute this value back into one of the original equations to solve for \( x \). We'll use the first equation:

\[
-5x + 4(2) = 48
\]
\[
-5x + 8 = 48
\]
\[
-5x = 48 - 8
\]
\[
-5x = 40
\]
\[
x = -8
\]

Thus, the solution to the system of equations is \( (x, y) = (-8, 2) \).

The final answer is:
\[
\boxed{(-8, 2)}
\]