__Solving Systems of Equations__

by Substitution

by Substitution

by Substitution

We can solve a systems of equations using substitution by isolating a variable in one of the given equations and plugging it into the other given equation.

As seen earlier, there are 3 types of solutions. When solving the systems of equations, there will either be one solution, no solutions, or infinitely many solutions.

Now in order to solve a system of equations by substitution, it is best to have one of the variables isolated so that we can plug it into the other equation.

Let's look at some examples:

Let's look at some examples:

The first thing that I notice from the system of equations is that both equations are in slope-intercept form

(y is solved for in both equations). This means that I can go straight into plugging in the value of one of the variables into the other equation.

(y is solved for in both equations). This means that I can go straight into plugging in the value of one of the variables into the other equation.

Now, in this systems of equations I notice that both equations do not have a variable isolated. I can decide if I would want to isolate either the x or y variable, and I can decide to isolate the variable in either equation. I am just going to choose to isolate y in the first equation. You should get the same answer regardless if you decided to isolate x, or isolated a variable in the second equation.

Click here to check your answer.

(C) 2017 MATH IN DEMAND