Example   Solve following systems.

(a)    3x - y = 7

                2x + 3 y = 1

Solution

Thus, it was the first system that we looked at above.  Already we know the solution, although it will give us a possibility to verify the values that we wrote down for the solution.

Now, the method says that we have to solve out one of the equations for one of the variables.  Which equation we select and which variable that we select is up to you, however usually it's best to pick an equation & variable which will be easy to deal with. It means we should try to ignore fractions if at all possible.

In this case it seem like it will be actually easy to solve the first equation for y thus let's do that.

                                              3x - 7 = y

 Substitute this into the second equation.

                   2 x + 3 (3x - 7 ) = 1

It is an equation in x which we can solve so let's do that.

2x + 9 x - 21 =1

11x = 22

x = 2

Thus, there is the x portion of the solution.

At last, do not forget to go back and determine the y portion of the solution. It is one of the more common mistakes students make in solving out systems.  To so it we can either plug the x value in one of the original equations & solve for y or we can only plug it into our substitution which we found in the initial step. That will be simple so let's do that.

                                          y = 3x - 7 = 3 ( 2) - 7 = -1

Thus, the solution is x = 2 and y = -1 as we noted above.