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