Question

Systems of Linear Equations Online Practice
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Question
Solve the system of equations.
x−3y=18

7x−5y=46
(1 point)
Responses

(33, 5)
(33, 5)
- incorrect

(−3, −5)
(−3, −5)
- no response given

(105, 5)
(105, 5)
- no response given

(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 these equations using substitution or elimination. Here, I'll use substitution.

From Equation 1, solve for \( x \):

\[
x = 3y + 18
\]

Now substitute \( x \) in Equation 2:

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

Expanding this:

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

Combine like terms:

\[
16y + 126 = 46
\]

Now isolate \( y \):

\[
16y = 46 - 126
\]
\[
16y = -80
\]
\[
y = -5
\]

Now substitute \( y \) back into the expression for \( x \):

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

So, the solution to the system of equations is \( (3, -5) \).

The correct answer is:

**(3, −5)**