Systems of Equations by Graphing and Substitution

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 for a system of equations to have one solution?

Back

The graphs of the equations intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

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

Back

The graphs of the equations are parallel and never intersect.

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CCSS.8.EE.C.8A

Front

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

Back

The graphs of the equations overlap each other completely.

Tags

CCSS.8.EE.C.8A

Front

How can you solve a system of equations by graphing?

Back

By plotting both equations on the same graph and identifying the point of intersection.

Tags

CCSS.8.EE.C.8B

Front

What is substitution in the context of solving systems of equations?

Back

Replacing one variable with an expression from another equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

If two lines are parallel, what can be said about their slopes?

Back

They have the same slope.

Tags

CCSS.8.EE.B.6

Front

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

Back

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

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

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

Back

By substituting the point's coordinates into both equations to see if they hold true.

Front

What is the graphical representation of the equation y = 2x + 1?

Back

A straight line with a slope of 2 and a y-intercept of 1.