Systems of Equations Basics Review

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What is a system of equations?

Back

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.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

It means the lines represented by the equations 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 no solution?

Back

It means the lines represented by 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 infinitely many solutions?

Back

It means the lines represented by the equations are the same line, so they intersect at every point on that line.

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CCSS.8.EE.C.8A

Front

How can you determine if a point is a solution to a system of equations?

Back

Substitute the x and y values of the point into both equations. If both equations are true, then the point is a solution.

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What is the slope of a line?

Back

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

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CCSS.8.EE.B.5

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What are parallel lines?

Back

Parallel lines are lines in a plane that never meet. They have the same slope.

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CCSS.HSG.CO.A.1

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What are perpendicular lines?

Back

Perpendicular lines are lines that intersect at a right angle. Their slopes are opposite reciprocals.

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CCSS.4.G.A.1

CCSS.HSG.CO.A.1

Front

How do you solve a system of equations by graphing?

Back

Graph both equations on the same coordinate plane and identify the point(s) where they intersect.

Tags

CCSS.8.EE.C.8B

Front

What is the substitution method for solving systems of equations?

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The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6