Question

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

x−5y=−20
(1 point)
Responses

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

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

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

(5, 3)

Answer 1

To solve the system of equations:

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

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

First, let's solve Equation 2 for \(x\):

\[
x = 5y - 20
\]

Now we can substitute \(x\) from Equation 2 into Equation 1:

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

Distributing the \(-4\):

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

Combining like terms:

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

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

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

Now, divide by \(-14\):

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

Now that we have \(y\), we can substitute it back into the expression we found for \(x\):

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

Thus, the solution to the system of equations is:

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

So the answer is:

\((−5, 3)\)