Solve the system of equations.

Question

x−3y=18

7x−5y=46
(1 point)
Responses

(−3, −5)
left parenthesis negative 3 comma negative 5 right parenthesis

(105, 5)
left parenthesis 105 comma 5 right parenthesis

(33, 5)
left parenthesis 33 comma 5 right parenthesis

(3, −5)

Answer 1

To solve the system of equations given by:

1. \( x - 3y = 18 \) (Equation 1)
2. \( 7x - 5y = 46 \) (Equation 2)

We will use the substitution method. First, we will solve Equation 1 for \( x \):

\[ x = 3y + 18 \]

Now we can substitute this expression for \( x \) into Equation 2:

\[ 7(3y + 18) - 5y = 46 \]

Distributing the 7:

\[ 21y + 126 - 5y = 46 \]

Combine like terms:

\[ 16y + 126 = 46 \]

Now, isolate \( y \):

\[ 16y = 46 - 126 \] \[ 16y = -80 \] \[ y = -5 \]

Now that we have \( y \), we can substitute it back into the expression we found for \( x \):

\[ x = 3(-5) + 18 \] \[ x = -15 + 18 \] \[ x = 3 \]

So the solution to the system of equations is \( (3, -5) \).

The correct response is:

(3, −5)