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:

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

We'll use the substitution or elimination method. Let's solve Equation 2 for \(x\):

From Equation 2:
\[
x = 5y - 20
\]

Now, substitute this expression for \(x\) in Equation 1:

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

Distribute \(-4\):
\[
-20y + 80 + 6y = 38
\]

Combine 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 \(y\), 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 from the options given is:
\[
\text{(−5, 3)}
\]