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Solve the system.

−5x+4y=48

−5x−8y=24
(1 point)
Responses

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

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

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

(−24,−18)

1 answer

To solve the system of equations:

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

  2. \(-5x - 8y = 24\) (Equation 2)

We can solve this system using the elimination method or substitution. Here, I will use elimination.

First, let's eliminate \( -5x \) by subtracting Equation 2 from Equation 1.

Subtract Equation 2 from Equation 1:

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

This simplifies to:

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

Combining the \(y\) terms gives:

\[ 12y = 24 \]

Now, divide both sides by 12:

\[ y = 2 \]

Now that we have \(y\), we substitute \(y = 2\) back into either Equation 1 or Equation 2 to find \(x\). Let's 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 of equations is:

\((-8, 2)\)

Thus, the answer is \((−8, 2)\).