Solve the system of equations.

3x - 4y = 40
5x - 5y = 55 (1 point)
• (14, 3)
O (18, 7)
• (4, -7)
• (8, -3)

1 answer

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)