Question

How do you solve `2x+3y=6` and `2x-y=-2` using substitution?

Answer 1

`(0,2)`

Explanation:

To solve by `color(blue)"substitution"`

Rearrange one of the equations in terms of x or y then substitute into the other equation and solve for x or y

`2x-y=-2to(1)`

`2x+3y=6to(2)`

Rearrange ( 1 ) to obtain y in terms of x , avoiding the use of fractions.

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

`color(blue)"Substitute "` into equation ( 2 )

`2x+3(color(red)(2x+2))=6larrcolor(red)" and solve for x"`

`rArr2x+6x+6=6`

`rArr8x+6=6`

subtract 6 from both sides.

`8xcancel(+6)cancel(-6)=6-6`

`rArr8x=0rArrx=0`

Substitute this value into ( 3 ) and evaluate for y

`x=0toy=0+2=2`

`rArr"point of intersection "=(0,2)`
graph{(y-2x-2)(y+2/3x-2)=0 [-10, 10, -5, 5]}