Question

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

x−5y=−20
(1 point)
Responses

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

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

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

(−35, −3)

Answer 1

To solve the system of equations:

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

We can solve it using the substitution or elimination method. Let's use the substitution method for simplicity.

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

\[
x = 5y - 20
\]

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

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

Expanding this gives:

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

Combining like terms:

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

Now, subtract 80 from both sides:

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

Dividing both sides by -14:

\[
y = 3
\]

Now that we have \( y \), we'll substitute it back into the equation for \( x \):

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

Thus, the solution to the system of equations is:

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

The correct response is:

\((−5, 3)\)