Question

Eliminate the y in the following system of equations. What is the result when you add the two equations?

x+y=2
3x-4y=27

Answer 1

thus: x = 5, y = -3

Explanation:

Solve the following system:

{y + x = 2 | (equation 1)

-4 y + 3 x = 27 | (equation 2)

Swap equation 1 with equation 2:

{3 x - 4 y = 27 | (equation 1)

x + y = 2 | (equation 2)

Subtract 1/3 × (equation 1) from equation 2:

{3 x - 4 y = 27 | (equation 1)

0 x + (7 y)/3 = -7 | (equation 2)

Multiply equation 2 by 3/7:

{3 x - 4 y = 27 | (equation 1)

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

Add 4 × (equation 2) to equation 1:

{3 x + 0 y = 15 | (equation 1)

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

Divide equation 1 by 3:

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

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

Collect results:

Answer: {x = 5, y = -3