Question

Solve the system of equations.
3x−4y=40

5x−5y=55
(1 point)
Responses

(18, 7)
left parenthesis 18 comma 7 right parenthesis

(14, 3)
left parenthesis 14 comma 3 right parenthesis

(4,−7)
left parenthesis 4 comma negative 7 right parenthesis

(8,−3)

Answer 1

To solve the system of equations given by:

1. \(3x - 4y = 40\) (Equation 1)
2. \(5x - 5y = 55\) (Equation 2)

First, let's simplify Equation 2:

\[
5x - 5y = 55 \implies x - y = 11 \implies x = y + 11 \quad \text{(Equation 3)}
\]

Now, we can substitute Equation 3 into Equation 1.

Substituting \(x = y + 11\) into Equation 1:

\[
3(y + 11) - 4y = 40
\]

Distributing:

\[
3y + 33 - 4y = 40
\]

Combining like terms:

\[
-y + 33 = 40
\]

To isolate \(y\), subtract 33 from both sides:

\[
-y = 7 \implies y = -7
\]

Now that we have \(y\), substitute it back into Equation 3 to find \(x\):

\[
x = y + 11 \implies x = -7 + 11 = 4
\]

So the solution to the system of equations is:

\[
(x, y) = (4, -7)
\]

Thus, the correct response is:

\((4, -7)\)