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? (1, 6) (6, 1) (7, 6) (6, 7)

Answer 1

The answer is (6, 7)

This is the system of two equations:
2y − x = 8
y − 2x = −5
_____
Express the second equation in the term of y:
2y - x = 8
y = 2x - 5
_____
Substitute y in the first equation:
2(2x - 5) - x = 8
4x - 10 - x = 8
4x - x = 10 + 8
3x = 18
x = 18/3
x = 6

Since x = 6 and y = 2x - 5, then:
y = 2 * 6 - 5 
y = 12 - 5
y = 7

Therefore, (x, y) = (6, 7)