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Solve the system.

−5x+4y=48

−5x−8y=24
(1 point)
Responses

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

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

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

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

1 answer

To solve the system of equations:

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

Let's start by eliminating \(x\) by subtracting Equation 1 from Equation 2.

  1. Rearranging both equations, we can align them for clarity:

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

Now, let's subtract the first equation from the second:

\[ (-5x - 8y) - (-5x + 4y) = 24 - 48 \] \[ -5x - 8y + 5x - 4y = -24 \] \[ -12y = -24 \]

Next, we solve for \(y\):

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

Now that we have \(y\), we can substitute it back into either Equation 1 or Equation 2 to find \(x\). We'll use Equation 1:

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

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

Thus, the correct response is:

\((-8, 2)\)