Question

A System of equations is shown.

{2x + 2y = 17
{4x - y = 25

What is the x-value of the solution to the system of equation?

Answer 1

x = 67/10 , y = 9/5

Explanation:

Solve the following system:

{2 x + 2 y = 17 | (equation 1)

4 x - y = 25 | (equation 2)

Swap equation 1 with equation 2:

{4 x - y = 25 | (equation 1)

2 x + 2 y = 17 | (equation 2)

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

{4 x - y = 25 | (equation 1)

0 x+(5 y)/2 = 9/2 | (equation 2)

Multiply equation 2 by 2:

{4 x - y = 25 | (equation 1)

0 x+5 y = 9 | (equation 2)

Divide equation 2 by 5:

{4 x - y = 25 | (equation 1)

0 x+y = 9/5 | (equation 2)

Add equation 2 to equation 1:

{4 x+0 y = 134/5 | (equation 1)

0 x+y = 9/5 | (equation 2)

Divide equation 1 by 4:

{x+0 y = 67/10 | (equation 1)

0 x+y = 9/5 | (equation 2)

Collect results:

Answer: x = 67/10 , y = 9/5