Question

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

5x−5y=55
(1 point)
Responses

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

(8,−3)
left parenthesis 8 comma negative 3 right parenthesis

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

(18, 7)

Answer 1

To solve the system of equations:

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

First, let's simplify Equation 2:

\[
5x - 5y = 55 \implies x - y = 11 \implies x = y + 11
\]

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

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

Expanding this gives:

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

Combining like terms:

\[
-y + 33 = 40
\]

Now, isolate \(y\):

\[
-y = 40 - 33
\]

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

Now, substitute \(y = -7\) back into \(x = y + 11\):

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

Thus, the solution to the system of equations is:

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

So the final answer is:

\((4, -7)\)