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

Answer 1

We have the system of equations:

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

To solve this system, we can first isolate one of the variables using either of the equations. Let's start with Equation 1 and solve for \(y\):

From Equation 1:
\[
-5x + 4y = 48
\]
Adding \(5x\) to both sides gives:
\[
4y = 5x + 48
\]
Now, divide by 4:
\[
y = \frac{5x + 48}{4}
\]

Next, we can substitute this expression for \(y\) into Equation 2:

Substituting \(y\) into Equation 2:
\[
-5x - 8\left(\frac{5x + 48}{4}\right) = 24
\]
Now, multiply each term in the equation by 4 to eliminate the fraction:
\[
-20x - 8(5x + 48) = 96
\]
Distributing \(-8\):
\[
-20x - 40x - 384 = 96
\]
Combining like terms:
\[
-60x - 384 = 96
\]
Adding 384 to both sides gives:
\[
-60x = 480
\]
Now divide by \(-60\):
\[
x = -8
\]

Now we can find \(y\) by substituting \(x = -8\) back into the expression for \(y\):
\[
y = \frac{5(-8) + 48}{4}
\]
Calculating inside the parentheses:
\[
y = \frac{-40 + 48}{4} = \frac{8}{4} = 2
\]

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

Hence, the answer is \((-8, 2)\).