Question

Solve the system of equations.
- 4x + 6y = 38
x — 5y =-20 (1 point)
О (35, - 3)
O (-5, 3)
О (5, 3)
• (-35, - 3)

Answer 1

To solve the system of equations:

1. \( -4x + 6y = 38 \)
2. \( x - 5y = -20 \)

We can use either substitution or elimination. Here, we'll use substitution for clarity.

First, let's solve the second equation for \( x \):

\[
x = 5y - 20
\]

Now, we substitute this expression for \( x \) into the first equation:

\[
-4(5y - 20) + 6y = 38
\]

Now, simplify it:

\[
-20y + 80 + 6y = 38
\]

Combine like terms:

\[
-20y + 6y + 80 = 38
\]
\[
-14y + 80 = 38
\]

Now, isolate \( y \):

\[
-14y = 38 - 80
\]
\[
-14y = -42
\]

Divide both sides by -14:

\[
y = 3
\]

Now that we have \( y \), we can find \( x \):

Substituting \( y = 3 \) back into the equation \( x = 5y - 20 \):

\[
x = 5(3) - 20
\]
\[
x = 15 - 20
\]
\[
x = -5
\]

So the solution to the system of equations is:

\[
(x, y) = (-5, 3)
\]

Verifying by substituting both values back into the original equations:

1. For the first equation:
\[
-4(-5) + 6(3) = 20 + 18 = 38 \quad \text{(True)}
\]

2. For the second equation:
\[
-5 - 5(3) = -5 - 15 = -20 \quad \text{(True)}
\]

Both equations are satisfied with this solution.

Thus, the answer is:

\[
\boxed{(-5, 3)}
\]