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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

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

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

(5, 3)

1 answer

To solve the system of equations:

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

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

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

\[x = 5y - 20\]

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

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

Expanding this gives:

\(-20y + 80 + 6y = 38\)

Now, combine like terms:

\(-20y + 6y + 80 = 38\)

\(-14y + 80 = 38\)

Now, let's isolate \(y\):

\(-14y = 38 - 80\)

\(-14y = -42\)

Dividing both sides by \(-14\):

\[y = 3\]

Now that we have \(y\), we can substitute it back into Equation 2 to find \(x\):

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

\[x = 15 - 20\]

\[x = -5\]

Thus, the solution to the system of equations is:

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

So the correct response is:

\((-5, 3)\)