Question

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

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

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

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 that we have the value of \(y\), we can substitute it back into the second equation to find \(x\):

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

Thus, the solution to the system of equations is:

\[
(x, y) = (-6, -1)
\]

Now we can check which given point matches this solution:

- (-7.25, -1.25) ➔ Not a solution
- (4, 1) ➔ Not a solution
- (-6, -1) ➔ This matches our solution
- (5.25, 1.25) ➔ Not a solution

The correct answer is:

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