Systems of Equations- Graphing & Word Problems

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What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What does it mean to graph a system of equations?

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It means to plot the equations on a coordinate plane to find their intersection point(s), which represent the solution(s).

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CCSS.8.EE.C.8B

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What is the solution to a system of equations?

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The point(s) where the graphs of the equations intersect, representing the values of the variables that satisfy all equations.

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CCSS.8.EE.C.8B

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What is an infinite number of solutions in a system of equations?

Back

This occurs when the equations represent the same line, meaning every point on the line is a solution.

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CCSS.8.EE.C.8B

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What does it mean if a system of equations has no solution?

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It means the lines are parallel and will never intersect, indicating there are no values that satisfy all equations.

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CCSS.8.EE.C.8A

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How do you determine the number of solutions in a system of equations?

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By analyzing the slopes and y-intercepts of the lines: if they are the same, infinite solutions; if slopes are different, one solution; if parallel, no solution.

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CCSS.8.EE.C.8B

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What is the slope-intercept form of a linear equation?

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The form is y = mx + b, where m is the slope and b is the y-intercept.

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CCSS.8.EE.B.6

CCSS.8.F.A.3

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How can you solve a system of equations by graphing?

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By graphing each equation on the same coordinate plane and identifying the point(s) where they intersect.

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CCSS.8.EE.C.8B

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What is a word problem in the context of systems of equations?

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A real-world scenario that can be modeled using a system of equations to find unknown values.

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CCSS.8.EE.C.8C

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How do you set up a system of equations from a word problem?

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Identify the variables, translate the relationships into equations, and write them as a system.

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CCSS.HSA.CED.A.3