Question

Solve the system of equations.
−4x+6y=38

x−5y=−20
(1 point)
Responses

(−5, 3)

(−35, −3)

(5, 3)

(35, −3)

Answer 1

To solve the system of equations given:

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

we can use the substitution or elimination method. Here, I'll use the elimination method.

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

\[
x = 5y - 20
\]

Now we can substitute \(x\) in the first equation:

Substituting \(x\) in the first equation:

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

Distributing \(-4\):

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

Combining like terms:

\[
-14y + 80 = 38
\]

Next, subtract \(80\) from both sides:

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

Now divide by \(-14\):

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

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

Using the equation \(x = 5y - 20\):

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

Now we have the solution:

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

Thus, the solution to the system of equations is:

\((-5, 3)\)