Solve the system of equations algebraically.

4x - 4y = - 48

5x - 6y = - 65

A) no solution

B) (-6, 4)

C) many solutions

D) (-7, 5)

x = - 7, y = 5 thus D)

Step-by-step explanation:

Solve the following system:

{4 x - 4 y = - 48 | (equation 1)

5 x - 6 y = - 65 | (equation 2)

Swap equation 1 with equation 2:

{5 x - 6 y = - 65 | (equation 1)

4 x - 4 y = - 48 | (equation 2)

Subtract 4/5 * (equation 1) from equation 2:

{5 x - 6 y = - 65 | (equation 1)

0 x + (4 y) / 5 = 4 | (equation 2)

Multiply equation 2 by 5/4:

{5 x - 6 y = - 65 | (equation 1)

0 x+y = 5 | (equation 2)

Add 6 * (equation 2) to equation 1:

{5 x+0 y = - 35 | (equation 1)

0 x+y = 5 | (equation 2)

Divide equation 1 by 5:

{x+0 y = - 7 | (equation 1)

0 x+y = 5 | (equation 2)

Collect results:

Answer: {x = - 7, y = 5