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June 17th

June 17th

# Graphing Systems of Equations

A set of equations with the same variables forms a system of equations . A solution to a system of two equations with two variables is an ordered pair of numbers that satisfies both equations. One way to solve a system of equations is to carefully graph the equations on the same coordinate plane. The coordinates of the point at which the graphs intersect is the solution to the system. If the graphs of the two equations coincide, meaning they are the same line, then there are infinitely many solutions to the system. A system of equations with at least one ordered pair that satisfies both equations is consistent. It is possible for the graphs of the two equations to be parallel. In this case, the system is inconsistent because there are no solutions that satisfy the two equations.

Example

Graph the system of equations to find the solution.

y = 2x - 3 and y = x - 1

The graphs appear to intersect at the point with coordinates (2, 1).

Check this estimate by replacing x with 2 and y with 1 in each equation.

Check:

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

The solution is (2, 1).

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