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

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

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

(105, 5)

1 answer

To solve the system of equations, we have:

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

First, we can solve the first equation for \( x \):

\[ x = 3y + 18 \]

Next, we can substitute this expression for \( x \) into the second equation:

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

Now, distribute \( 7 \):

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

Combine like terms:

\[ 16y + 126 = 46 \]

Subtract 126 from both sides:

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

Now, divide by 16:

\[ y = -5 \]

Now that we have \( y \), we can substitute \( y = -5 \) back into our expression for \( x \):

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

So, the solution to the system of equations is:

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

The answer to the system of equations is

\[ \boxed{(3, -5)} \]