Question

How do you solve `8x + 7y = 25` and `x = 25 - 4y` using substitution?

Answer 1

`(x,y)to(-3,7)`

Explanation:

`8x+7y=25to(1)`

`x=25-4yto(2)`

`"substitute "x=25-4y" into equation "(1)`

`8(25-4y)+7y=25`

`rArr200-32y+7y=25`

`rArr200-25y=25`

`"subtract 200 from both sides"`

`cancel(200)cancel(-200)-25y=25-200`

`rArr-25y=-175`

`"divide both sides by "-25`

`(cancel(-25) y)/cancel(-25)=(-175)/(-25)`

`rArry=7`

`"substitute " y=7" into equation "(2)`

`x=25-(4xx7)=25-28=-3`

`rArr"point of intersection "=(-3,7)`