Question

Solve the system of equations. 2x+6y=−18 x=5y−1 (1 point)

(5.25, 1.25)

(−7.25, −1.25) left parenthesis negative 7.25 comma negative 1.25 right parenthesis

(4, 1) left parenthesis 4 comma 1 right parenthesis

(−6, −1)

Answer 1

To solve the system of equations, we have:

1. \( 2x + 6y = -18 \) (Equation 1)
2. \( x = 5y - 1 \) (Equation 2)

We'll substitute Equation 2 into Equation 1.

Substituting \( x \) in Equation 1:
\[
2(5y - 1) + 6y = -18
\]

Now, distribute the 2:
\[
10y - 2 + 6y = -18
\]

Combine like terms:
\[
16y - 2 = -18
\]

Add 2 to both sides:
\[
16y = -16
\]

Now divide by 16:
\[
y = -1
\]

Next, substitute \( y \) back into Equation 2 to find \( x \):
\[
x = 5(-1) - 1 = -5 - 1 = -6
\]

So the solution to the system of equations is:
\[
(x, y) = (-6, -1)
\]

Now we will compare our results with the provided options:

- (5.25, 1.25)
- (−7.25, −1.25)
- (4, 1)
- (−6, −1)

The correct solution is \((-6, -1)\).