Solve the system of equations. x−3y=18 7x−5y=46 (1 point) Responses (−3, −5) left parenthesis negative 3 comma negative 5 right parenthesis (3, −5) left parenthesis 3 comma negative 5 right parenthesis (33, 5) left parenthesis 33 comma 5 right parenthesis (105, 5)

Answer 1

To solve the system of equations:

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

We can solve this system using substitution or elimination. Here, I'll use substitution.

First, solve Equation 1 for \( x \):

\[ x = 3y + 18 \]

Now substitute \( x \) from this equation into Equation 2:

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

Expanding this:

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

Combining like terms:

\[ 16y + 126 = 46 \]

Now, isolate \( y \):

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

Now substitute \( y = -5 \) back into the expression for \( x \):

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

Thus, the solution to the system of equations is:

\[ (x, y) = (3, -5) \]

So the correct response is \( (3, -5) \).