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Published byColin Bryant Modified over 8 years ago

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Objective The student will be able to: solve systems of equations by graphing.

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What is a system of equations? A system of equations is when you have two or more equations using the same variables. A system of two linear equations in two variables x and y has the form: y = mx + b A solution to a system of linear equations in two variables is an ordered pair that satisfies both equations in the system. When graphing, you will encounter three possibilities.

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Solving a system of linear equations by graphing Rewrite each equation in slope- intercept form – y=mx + b. Determine the slope and y-intercept and use them to graph each equation. The solution to the linear system is the ordered pair where the lines intersect.

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

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Y = 1/2x + 5 Y = -5/2x - 1 Examples

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Y = -3/2x + 1 Y = 1/2x - 3 Examples

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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.

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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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Y = 2/3x - 5 Y = 2/3x + 1 How many solutions?

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Y = 3x - 12 Y = 1/8x - 12 How many solutions?

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Y = 5/3x - 2 Y = 10/6x - 2 How many solutions?

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Solving a system of equations by graphing. Let's summarize! There are 3 steps to solving a system using a graph. Step 1: Graph both equations. Step 2: Do the graphs intersect? Step 3: Check your solution. Graph using slope and y – intercept or x- and y-intercepts. Be sure to use a ruler and graph paper! This is the solution! LABEL the solution! Substitute the x and y values into both equations to verify the point is a solution to both equations.

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