Question

Solve the system of equations. x−3y=18 7x−5y=46

(−3, −5)

(33, 5)

(105, 5)

(3, −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 using the substitution or elimination method. Here, I’ll use the substitution method.

From Equation 1, we can express \( x \) in terms of \( y \):

\[
x = 3y + 18
\]

Now, we substitute \( x \) into Equation 2:

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

Expanding this:

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

Combining like terms:

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

\[
16y + 126 = 46
\]

Now, isolate \( y \):

\[
16y = 46 - 126
\]

\[
16y = -80
\]

Dividing by 16:

\[
y = -5
\]

Now that we have \( y \), we can find \( x \) using Equation 1:

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

\[
x = -15 + 18
\]

\[
x = 3
\]

So the solution to the system of equations is:

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

Thus, the correct answer is:

**(3, −5)**.