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.
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.
Solve Systems of Three Equations
First Variable Easy to Find
Solve Systems of Three Variables Eliminating First Variable is Easy
Solve Systems of Three Equations Must Multiply to Eliminate First Variable
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.
Application: Ticket Prices
Word Problem Involving Difference, Product and Sum of Reciprocals