Using substitution is another methed used to solve Linear Systems... sometimes the easiest way. It is another option for people who do not want to draw out graphs to solve every system. Substitution can be used to solve real life problems such as in comparing costs and investments, that is one of the reasons this is so important to learn. I hope you enjoy learning how to use substitution to solve linear systems because your off, the race has begun!!!

The steps to using Substitution:

1) First you must solve one of the equations for just one of its variables.

2) Next you substitute the answer you recieve/expression into the second equation and solve for the other variable.

3) After doing this you should have the solution for one of the variables, and a expression representing the other variable. In the first equation that you solved, substitute the definite solution that you have reached for one variable into its place, and solve to find out the other variable.

4) Last you must check the ordered pair you have recieved in BOTH of the original equations to make sure it is correct.

Examples:

Ex1) .. x=y+0 (y+0)+y=2 2y=2 y=1 x-1=0 x=1

(1, 1)

Check: 1-1=0, yes 1+1=2, yes

Ex2) y= -2x+4 -x+(-2x+4)=1 -3x+4=1 -3x=-3 x=1

2(1)+y=4 2+y=4 y=2

(1, 2)

Check: 2(1)+2=4, yes -1+4=1, yes

Ex3) . y=-x+1 2x-(-x+1)=2 3x-1=2 3x=3 x=1 1+y=0 y=0

(1, 0)

Check: 1+0=1, yes 2(1)-0=2, yes

Now you know how to solve Linear Systems using the Substitution method!!!