Question

Solve the system.
−5x+4y=48

−5x−8y=24
(1 point)
Responses

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

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

(−24,−18)
left parenthesis negative 24 comma negative 18 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 eliminate \(x\) by subtracting Equation 2 from Equation 1:

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

Simplifying this gives:

\[
4y + 8y = 24
\]

\[
12y = 24
\]

Now, divide both sides by 12:

\[
y = 2
\]

Now that we have \(y\), we can substitute this value back into one of the original equations to find \(x\). We can use Equation 1:

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

This simplifies to:

\[
-5x + 8 = 48
\]

Subtract 8 from both sides:

\[
-5x = 40
\]

Now, divide by -5:

\[
x = -8
\]

So the solution to the system is:

\[
(-8, 2)
\]

Thus the correct response is:

\((−8, 2)\)