Question

What is the solution to the system of equations?

6x+2y = 6
7x+3y=5
(-3, 2)
(-1,6)
(2, -3)
(6, -1)

Answer 1

x = 2 , y = -3

Explanation:

Solve the following system:

{6 x + 2 y = 6 | (equation 1)

7 x + 3 y = 5 | (equation 2)

Swap equation 1 with equation 2:

{7 x + 3 y = 5 | (equation 1)

6 x + 2 y = 6 | (equation 2)

Subtract 6/7 × (equation 1) from equation 2:

{7 x + 3 y = 5 | (equation 1)

0 x - (4 y)/7 = 12/7 | (equation 2)

Multiply equation 2 by 7/4:

{7 x + 3 y = 5 | (equation 1)

0 x - y = 3 | (equation 2)

Multiply equation 2 by -1:

{7 x + 3 y = 5 | (equation 1)

0 x+y = -3 | (equation 2)

Subtract 3 × (equation 2) from equation 1:

{7 x+0 y = 14 | (equation 1)

0 x+y = -3 | (equation 2)

Divide equation 1 by 7:

{x+0 y = 2 | (equation 1)

0 x+y = -3 | (equation 2)

Collect results:

Answer: {x = 2 , y = -3