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

Answer: The correct answer is (6, 7).

We can solve this system of equation by elimination.

2y - x = 8
y - 2x = -5 Multiply this row by -2

2y - x = 8
-2y + 4x = 10 Add

3x = 18
x = 6

Now, input 6 into either equation and you will get y = 7.
Therefore, the solution to the equation is (6, 7).

Answer 2

(6,7)

Explanation:

Given :
`2y- x = 8`

`y - 2x = -5`

Solution:

`2y- x = 8` --A

`y - 2x = -5` ---B

Substitute value of y from B in A

`2(-5+2x)- x = 8`

`-10+4x- x = 8`

`-10+3x = 8`

`3x = 18`

`x = (18)/(3)`

`x = 6`

Substitute the value of x in A to get value of y.

`2y- 6 = 8`

`2y=14`

`y=(14)/(2)`

`y=7`

Thus the solution to the given system of equations is (6,7).