Rearranging Before Substitution
In substitution problems we have two equations that each have the same two variables.
We then substitute what x is equal to in the bottom equation in place of the x in the top equation.
Then we solve:
Then we plug our value of y into either of the two original equations and solve for x.
So our ordered pair (x,y) is: (-1.857,2.571)
But what if neither of our two original equations is solved for one of our variables? Then we have to solve one of the equations for one of the variables to use substitution.
We need to solve one of the equations for one of our variables. It doesn't matter which one we choose.
The bottom one looks easier so let's pick it.
2x-4y=8 Then solve it for x.
Now our system of equations is:
We plug in 2y+4 for the x in the top equation.
3(2y+4)-2y=5 and solve for y.
Then we plug our value for y into either of our two original equations and solve for x.
So our ordered pair (x,y) is (.5,-1.75)