SYSTEMS OF EQUATIONS

Solve Systems of Equations Graphically

Learn to solve systems of equations by graphing. This method is great when the intersection point is an integer. The downside to this method is that, if the lines intersect at a decimal, it is not easy to see the intersection point without technology.

In Slope-Intercept Form
In Standard Form
Using the TI-84
Using the TI-Nspire

Solve Systems of Equations by Substitution

Learn to solve systems of equations by substitution. This method is best to use when one variable is already solved for or one variable has a coefficient of 1. If both variables have coefficients other than 1, it is best to use the elimination method.

Both Equations Solved for y
One Equation Solved for y
Neither Equation Has a Variable Solved for

Solve Systems of Equations by Elimination

Learn to solve systems of equations by elimination. This method is best to use when both variables are on the same side, and the constant terms are on the opposite. This method eliminates one of the variables by getting the numbers in front of one variable to be opposites of each other, and then adding the equations together.

Add to Eliminate (Easy)
Subtract to Eliminate (Easy)
Multiply One Equation to Eliminate
Multiply Both Equations to Eliminate

Solve Systems of Three Equations

Learn to solve systems of three equations. This can be very time consuming, and is a process that can get overwhelming. The more you practice, and the neater the work, the easier these problems will get.

First Variable Easy to Find
Eliminating First Variable is Easy
Must Multiply to Eliminate First Variable

Solve Systems with Nonlinear Equations

Learn to solve systems of equations that contain nonlinear equations. These can include equations of circles, ellipses, parabolas, and hyperbolas. Some of these have to be solved with substitution, while others can be solved with elimination.

Solve Using Substitution -Line and Ellipse
Solve Using Elimination -Circle and Ellipse

Systems of Equations Word Problems

Learn to solve word problems involving systems of equations. There are many applications of systems of equations, and knowing how to solve them can be beneficial.

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