Question

Solve the system of equations.
-4x + 6y = 38
x — 5y =-20 (1 point)
О (35, - 3)
• (-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 the substitution or elimination method. Here, I will use the substitution method.

First, we can solve the second equation for \(x\):

\[
x = 5y - 20
\]

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

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

Distributing \(-4\):

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

Combining like terms:

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

Now, isolate \(y\):

\[
-14y = 38 - 80
\]
\[
-14y = -42
\]
\[
y = \frac{-42}{-14} = 3
\]

Now that we have \(y\), we can substitute \(y = 3\) back into the equation for \(x\):

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

So, the solution to the system of equations is:

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

Thus, the answer is:

• \((-5, 3)\)