Question

Solve the system of equations algebraically.

4x – 4y = –48

5x – 6y = –65



A) no solution

B) (–6, 4)

C) many solutions

D) (–7, 5)

Answer 1

x = -7 , y = 5 thus D)

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