Solve the system of two linear equations.

Question

−3x−4y=−23
3x−5y=5 (1 point)
Responses

(5, 2)
left parenthesis 5 comma 2 right parenthesis

(−5, 2)
left parenthesis negative 5 comma 2 right parenthesis

(−5,−2)
left parenthesis negative 5 comma negative 2 right parenthesis

(5,−2

Answer 1

To solve the system of equations:

1. Equation 1: \(-3x - 4y = -23\)
2. Equation 2: \(3x - 5y = 5\)

We'll use the method of substitution or elimination. Here, we will use elimination.

First, we can manipulate the equations to eliminate one variable. Let's multiply Equation 2 by 1, and add both equations:

\[ -3x - 4y = -23 \] \[ 3x - 5y = 5 \]

Now, let's add these equations together:

1. When adding \( -3x + 3x \) we get \( 0 \).
2. When adding \( -4y - 5y \) we get \( -9y \).
3. When adding \( -23 + 5 \) we get \( -18 \).

Thus, we have:

\[ -9y = -18 \]

Now, solve for \( y \):

\[ y = \frac{-18}{-9} = 2 \]

Now that we have \( y = 2 \), we can substitute it back into one of the original equations to find \( x \). Let's use Equation 2:

\[ 3x - 5y = 5 \]

Substituting \( y = 2 \):

\[ 3x - 5(2) = 5 \] \[ 3x - 10 = 5 \] \[ 3x = 5 + 10 \] \[ 3x = 15 \] \[ x = \frac{15}{3} = 5 \]

Thus, the solution to the system of equations is \( (x, y) = (5, 2) \).

Therefore, the correct response is:

\((5, 2)\)