Question

page 9 of 9
Solving Equations Using Substitution Quick Check
4 of 54 of 5 Items






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 5 comma 3 right parenthesis

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

(−5, 3)

Answer 1

To solve the system of equations using substitution, we have the following equations:

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

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

\[
x = 5y - 20
\]

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

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

Distribute \(-4\):

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

Combine like terms:

\[
-14y + 80 = 38
\]

Now, isolate \( y \):

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

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

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

So the solution to the system of equations is \( (x, y) = (-5, 3) \).

The correct response is:

**(−5, 3)**.