Identifying Solutions to Systems of Equations

Front

What is a system of equations?

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

The lines representing the equations are parallel and never intersect.

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CCSS.8.EE.C.8A

Front

What does it mean if a system of equations has one solution?

Back

The lines intersect at exactly one point.

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CCSS.8.EE.C.8A

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The lines are the same, meaning they overlap completely.

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CCSS.8.EE.C.8A

Front

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

Back

By comparing the slopes and y-intercepts of the equations.

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CCSS.8.EE.C.8B

Front

What is the slope of a line?

Back

The steepness of the line, calculated as the rise over run.

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CCSS.8.EE.B.5

Front

If two lines have the same slope but different y-intercepts, what can be said about their solutions?

Back

They have no solutions because they are parallel.

Tags

CCSS.8.EE.C.8B

Front

If two lines have different slopes, what can be said about their solutions?

Back

They have one solution where they intersect.

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CCSS.8.EE.C.8A

Front

What is the graphical representation of a system of equations?

Back

It is represented by the intersection of lines on a coordinate plane.

Tags

CCSS.8.EE.C.8A

Front

What is the significance of the y-intercept in a linear equation?

Back

It is the point where the line crosses the y-axis.