Solve the system of equations.

Question

−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).