Question

What is the solution to -2x+4y=16 2x+2y=8

Answer 1

Greetings!

To solve this, you can multiply one of the equations by a number so that one of the unknown values are the same as the other equation. Or simply in these two equations you can multiply the second equation by a minus (-1):

(2x + 2y = 8 ) x -1

= -2x - 2y = -8

Now, you can add or minus the two equations, but seeing as both values before the x are negative we can add the two equations to cancel out the x:

-2x + 4y = 16 +

-2x = 2y = -8

= 0x + 6y = 8

6y = 8

Simply divide 8 by 6 to find y:

8 ÷ 6 =
`(4)/(3)` , so the value of y =
`(4)/(3)`

Now you can substitute this value into one of the equations:

2x + 2y = 8

2x + 2(
`(4)/(3)`) = 8

2x +
`(8)/(3)` = 8

2x = 8 -
`(8)/(3)`

2x =
`(16)/(3)`

x =
`(16)/(3)` ÷ 2

x =
`(8)/(3)`

So that means x =
`(8)/(3)` and y =
`(4)/(3)`

Hope this helps!