How To: Solve a system of equations in algebra

In this math lesson you will learn how to solve a system of equations. Watch the following video to learn how to translate a word problem into a system of linear equations.

Two linear equations considered in the same time form a system of linear equations. A system of linear equations can have one solution, an infinite number of solutions, or no solution. Since the graph of any linear equation is a line, the solution of a system of linear equations is given by the point of intersection between the two lines. If the two lines are parallel, the system has no solution.

There are several ways of finding the solution:

• Graph each equation and find the intersection point.

• Write one of the two variables in terms of the other one, and substitute it in one of the equations. The resulting equation will have only one unknown.

• When possible, add or subtract the two equations to eliminate of one of the variables. This method only works if the coefficients of a variable are equal or opposite numbers.