Question

solve the system of equations

2x + 6y = -18
x = 5y - 1

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

Answer 1

To solve the system of equations, we will substitute the value of \( x \) from the second equation into the first equation.

The equations are:
1. \( 2x + 6y = -18 \)
2. \( x = 5y - 1 \)

Substituting equation (2) into equation (1):

\[
2(5y - 1) + 6y = -18
\]

Now, distribute \( 2 \):

\[
10y - 2 + 6y = -18
\]

Combine like terms:

\[
16y - 2 = -18
\]

Now, add \( 2 \) to both sides:

\[
16y = -16
\]

Divide both sides by \( 16 \):

\[
y = -1
\]

Now, substitute \( y = -1 \) back into equation (2) to find \( x \):

\[
x = 5(-1) - 1
\]

Calculating this gives:

\[
x = -5 - 1 = -6
\]

So, the solution of the system of equations is \( (x, y) = (-6, -1) \).

Now let's check if this solution is among the provided options:

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

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