Solve the system of equations.

Question

−4x+6y=38

x−5y=−20
(1 point)
Responses

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

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

Let's solve these equations step by step.

First, we can solve Equation 2 for \(x\):

\[ x = 5y - 20 \]

Now we can substitute this expression for \(x\) back into Equation 1:

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

Expanding this:

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

Combining like terms:

\[ -14y + 80 = 38 \]

Now, isolate \(y\):

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

Dividing by \(-14\):

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

Now that we have \(y\), substitute it back into the expression 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 correct response is:

\((−5, 3)\)