# use elimination and substitution to solve for 'x' and 'y' for simultaneous linear equation y=x y=-3x-8. How is this done?

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

Solve the system `y=x` and `y=-3x-8` :

(1) Using substitution: Since `y=x` from the first equation, we can substitute x for y in the second equation. This gives us:

`x=-3x-8`

`4x=-8`

`x=-2`

Since y=x, we have y=-2

The solution is (-2,-2)

Check: -2=-2 is true, and -2=-3(-2)-8 is true

(2) Using elimination:

Write each equation in the same form (slope-intercept, intercept, standard form, etc...). Here:

`y=x`

`y=-3x-8`

We can add or subtract the two equations, and we can add a multiple of one equation to a multiple of the other equation. The goal is to eliminate one of the variables. (This method is also called the multiplication/addition method, or linear combinations). Here subtract the first equation from the second to get:

`0=-4x-8`

`4x=-8`

`x=-2` , and since `y=x,y=-2` as before.

(3) The graphs: the solution is the intersection point

Sources: