Solving Systems of Equations by Graphing

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What is a system of equations?

Back

A set of two or more equations with the same variables.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What does it mean for a system of equations to have no solution?

Back

It means that the lines represented by the equations are parallel and never intersect.

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CCSS.8.EE.C.8A

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What does it mean for a system of equations to have one solution?

Back

It means that the lines represented by the equations intersect at exactly one point.

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CCSS.8.EE.C.8A

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What does it mean for a system of equations to have infinitely many solutions?

Back

It means that the equations represent the same line, so every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

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How do you graph a linear equation?

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You can graph a linear equation by finding two or more points that satisfy the equation and connecting them with a straight line.

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What is the graphical representation of the solution to a system of equations?

Back

The point(s) where the graphs of the equations intersect.

Tags

CCSS.8.EE.C.8B

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What is the slope of a line?

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The slope is a measure of the steepness of a line, calculated as the rise over run (change in y over change in x).

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CCSS.8.EE.B.5

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How can you determine if a system of equations has no solution by graphing?

Back

If the lines are parallel, they will never intersect, indicating no solution.

Tags

CCSS.8.EE.C.8A

Front

How can you determine if a system of equations has infinitely many solutions by graphing?

Back

If the lines overlap completely, they represent the same line, indicating infinitely many solutions.

Tags

CCSS.8.EE.C.8A

Front

What is the solution to the system of equations: y = 2x + 1 and y = 2x - 3?

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No solution (the lines are parallel).

Tags

CCSS.8.EE.C.8B