Question

How do you solve `3x-2y=2` and `-2x+y=8` using substitution?

Answer 1

`(x,y)to(-18,-28)`

Explanation:

`3x-2color(red)(y)=2to(1)`

`-2x+color(red)(y)=8to(2)`

`"from "(2)color(white)(x)color(red)(y)=8+2xto(3)`

`"substitute "y=8+2x" in "(1)`

`rArr3x-2(8+2x)=2`

`rArr3x-16-4x=2`

`rArr-x=18rArrx=-18`

`"substitute this value in "(3)`

`rArry=8+(2xx-18)=8-36=-28`

`color(blue)"As a check"`

`"Substitute these values in "(1)`

`(3xx-18)-(2xx-28)=-54+56=2larr" True"`

`rArr" point of intersection "=(-18,-28)`