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

Let's first solve the second equation for \(x\):

\[x = 5y - 20\]

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

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

Distributing \(-4\):

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

Combine like terms:

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

\[-14y + 80 = 38\]

Now, isolate \(y\):

\[-14y = 38 - 80\] \[-14y = -42\] \[y = \frac{-42}{-14} = 3\]

Now that we have \(y\), we can find \(x\) using the expression we found earlier:

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

\[x = 15 - 20\]

\[x = -5\]

So the solution to the system of equations is \((-5, 3)\).

Thus, the correct response is:

\((−5, 3)\)