Question

Solve equations `y=2x-13` and `y=-2x+23` by elimination method?

Answer 1

`x=9` and `y=5`

Explanation:

As `y=2x-13` and

`y=-2x+23`

Just adding them gives `2y=2x-13-2x+23=10`

Hence `y=10/2=5` and putting this in first equation, we get

`5=2x-13`

or `2x=5+13=18`

Hence `x=18/2=9`

Answer 2

`x=9 and y =5`

Explanation:

`y = 2x-13 and y = -2x+23`

This is the best scenario you can get if you want to use the elimination method.

Notice that the two `x=`terms are additive inverses.

`y = color(blue)(2x)-13 and y = color(blue)(-2x)+23`

If you add the two equations together, the `x-`terms will add up to 0 and thereby be eliminated.

`color(white)(...........)y =" " 2x-13 ............................A`
`color(white)(...........)y = -2x+23 ............................B`

`A+B:" :2y = color(blue)(0x) +10`
`color(white)(..............)y = 5`

Substitute to find `x`

`color(white)(.............)5 = 2x-13 ............................A`
`color(white)(.....)5+13 =2x`
`color(white)(.............)18 =2x`
`color(white)(...............)9 =x`

Check in B

`color(white)(...........)y = -2(9)+23 ............................B`
`color(white)(...........)y = -18+23`
`color(white)(...........)y = 5`