Question

How do you solve the system `x=y-5` and `3x+2y=3` by substitution?

Answer 1

`(x,y)to(-7/5,18/5)`

Explanation:

`x=y-5to(1)`

`3x+2y=3to(2)`

`"equation "(1)" expresses x in terms of y"`

`color(blue)"Substitute "x=y-5" into equation "(2)`

`3(y-5)+2y=3`

`rArr3y-15+2y=3`

`rArr5y-15=3`

`"add 15 to both sides"`

`5ycancel(-15)cancel(+15)=3+15`

`rArr5y=18`

`"divide both sides by 5"`

`(cancel(5) y)/cancel(5)=18/5`

`rArry=18/5`

`"substitute "y=18/5" in equation "(1)`

`rArrx=18/5-5=18/5-25/5=-7/5`

`"solution is "(x,y)to(-7/5,18/5)`