Question

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?

Answer 1

x=6 y =7

Explanation:

Answer 2

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