Question

Solve the system of equations.
3x - 4y = 40
5x - 5y = 55 (1 point)
• (14, 3)
O (18, 7)
• (4, -7)
• (8, -3)

Answer 1

To solve the system of equations, we have:

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

First, we can simplify the second equation:

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

Now, we substitute \(x = y + 11\) into the first equation:

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

Expanding this gives:

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

Combining like terms results in:

\[
-y + 33 = 40 \implies -y = 40 - 33 \implies -y = 7 \implies y = -7
\]

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

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

Thus, the solution to the system of equations is:

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

Among the given options, the correct solution is:

• (4, -7)