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Solve the system.

−5x+4y=48

−5x−8y=24
(1 point)
Responses

(−8, 2)
(−8, 2)
- no response given

(8, 2)
(8, 2)
- no response given

(−24,−18)
open paren negative 24 comma negative 18 close paren - no response given

(24,−18)
open paren 24 comma negative 18 close paren - incorrect
R

1 answer

To solve the given system of equations:

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

We can solve this system using the elimination method.

First, let's manipulate the equations to eliminate \(x\). We can subtract Equation 2 from Equation 1.

Subtracting Equation 2 from Equation 1:

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

This simplifies to:

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

\[ 12y = 24 \]

Now, divide both sides by 12:

\[ y = 2 \]

Now that we have \(y\), we can substitute it back into one of the original equations to find \(x\). Let's use Equation 1:

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

This simplifies to:

\(-5x + 8 = 48\)

Now, subtract 8 from both sides:

\(-5x = 40\)

Now, divide by -5:

\[ x = -8 \]

So, the solution to the system is:

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

The correct response is \((-8, 2)\).