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

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

(5, 3)

Answer 1

To solve the system of equations:

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

We can use substitution or elimination. Let's use substitution for this example.

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

\[
x = -20 + 5y
\]

Now, substitute \(x\) into the first equation:

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

Distribute \(-4\):

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

Combine like terms:

\[
80 - 14y = 38
\]

Now, isolate \(y\):

\[
-14y = 38 - 80
\]
\[
-14y = -42
\]
\[
y = 3
\]

Now, substitute \(y = 3\) back into the equation for \(x\):

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

Thus, the solution is \((-5, 3)\).

So the answer is:

**(−5, 3)**.