Question

Solve the system of equations.
−4x+6y=38
x−5y=−20 (1 point)
Responses

(35, −3)
left parenthesis 35 comma negative 3 right parenthesis

(−5, 3)
left parenthesis negative 5 comma 3 right parenthesis

(5, 3)
left parenthesis 5 comma 3 right parenthesis

(−35, −3)

Answer 1

To solve the system of equations

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

we can use substitution or elimination. Here, we will use substitution.

From equation (2), we can express \( x \) in terms of \( y \):

\[
x = 5y - 20
\]

Now, we substitute this expression for \( x \) into equation (1):

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

Distributing \(-4\):

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

Combine like terms:

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

Now isolate \( y \):

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

Dividing both sides by \(-14\):

\[
y = 3
\]

Now substitute \( y \) back into the expression we found for \( x \):

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

Thus, the solution to the system is:

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

The correct response is:

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