Question

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)

Answer 1

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

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