The table can be used to determine the solution to the system of equations, 2y - x = 8, and y - 2x = - 5.

Which solution can be used to fill in both blanks in the table?

Determine the given

2y - x = 8 ⇒ equation 1

y - 2x = - 5 ⇒ equation 2

Get y equivalent from equation 2:

y = 2x - 5 ⇒ equation 3

Substitute y = 2x - 5 to equation 1

2 (2x-5) - x = 8

Distribute and Simplify

4x - 10 - x = 8

3x = 10 + 8 ⇒ combine like terms by transposing it to other side

3x = 18

x = 6 ⇒ divide both sides by 3 to get the value of x

Substitute the value of x to equation 3

y = 2 (6) - 5

y = 12 - 5

y = 7

Answer : x = 6; y = 7