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Understanding Systems of Equations: Graphing and Solutions

Learn about systems of equations and how to find their solutions through graphing. Discover the different possibilities such as intersecting lines, parallel lines, and coinciding lines.

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Understanding Systems of Equations: Graphing and Solutions

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  1. What is a system of equations? • A system of equations is when you have two or more equations using the same variables. • The solution to the system is the point that satisfies ALL of the equations. This point will be an ordered pair. • When graphing, you will encounter three possibilities.

  2. The Slope-Intercept Formula

  3. Intersecting Lines • The point where the lines intersect is your solution. • The solution of this graph is (1, 2) (1,2)

  4. Parallel Lines • These lines never intersect! • Since the lines never cross, there is NO SOLUTION! • Parallel lines have the same slope with different y-intercepts.

  5. Coinciding Lines • These lines are the same! • Since the lines are on top of each other, there are INFINITELY MANY SOLUTIONS! • Coinciding lines have the same slope and y-intercepts.

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