Question

Solve the system of equations.
x−3y=18

7x−5y=46
(1 point)
Responses

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

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

(−3, −5)
left parenthesis negative 3 comma negative 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'll solve it step by step.

First, let's solve Equation 1 for \( x \):

\[
x = 3y + 18
\]

Now, we substitute \( x \) in Equation 2 with \( 3y + 18 \):

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

Expanding the equation:

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

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 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 answer is \((3, -5)\).