Question

Solve the system of equations.
2х + 6y = - 18
x = 5y - 1 (1 point)
O (-6, - 1)
• (5.25, 1.25)
O (4, 1)
O (-7.25, - 1.25)

Answer 1

To solve the system of equations

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

we can substitute the expression for \( x \) from the second equation into the first equation.

Substitute \( x = 5y - 1 \) into the first equation:

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

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 \( y = -1 \) back into the second equation to find \( x \):

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

\[
x = -5 - 1
\]

\[
x = -6
\]

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

Now, let's check if this solution matches one of the options given:

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

Thus, the solution to the system of equations is:

\[
\boxed{(-6, -1)}
\]