Systems of Equations- Graphing & Word Problems

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What is a system of equations?

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A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect on a graph.

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CCSS.8.EE.C.8B

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

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A system has no solution when 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?

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A system has one solution when 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?

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A system has infinitely many solutions when the equations represent the same line, meaning they overlap completely.

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CCSS.8.EE.C.8A

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How do you graph a linear equation?

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To graph a linear equation, identify the y-intercept and slope, plot the y-intercept on the graph, and use the slope to find another point.

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

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The slope-intercept 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 determine the point of intersection of two lines graphically?

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The point of intersection is where the two lines cross on the graph. This point represents the solution to the system of equations.

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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 word problem is a real-life 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 and conditions into equations, and write them as a system.

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CCSS.8.EE.C.8C

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What is the importance of finding the point of intersection in a word problem?

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Finding the point of intersection helps determine the values that satisfy all conditions of the problem.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6