Solving Systems of Equations by Graphing

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 no solution?

Back

It means that the lines representing the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

What does it mean for a system of equations to have one solution?

Back

It means that the lines representing 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 infinitely many solutions?

Back

It means that the lines representing the equations are the same line, overlapping completely.

Tags

CCSS.8.EE.C.8A

Front

How do you graph a linear equation?

Back

You can graph a linear equation by finding two or more points that satisfy the equation and connecting them with a straight line.

Front

What is the solution to the system of equations represented by the lines y = 2x + 1 and y = -x + 3?

Back

(2, 5) is the solution, where the two lines intersect.

Tags

CCSS.8.EE.C.8B

Front

What is the slope of the line represented by the equation y = 3x + 2?

Back

The slope is 3.

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CCSS.8.EE.B.5

Front

What is the y-intercept of the line represented by the equation y = -2x + 4?

Back

The y-intercept is 4.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

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

Back

Substitute the point's coordinates into each equation; if both equations are true, the point is a solution.

Front

What happens when you graph the same equation twice?

Back

You will have infinitely many solutions, as the lines will overlap.

Tags

CCSS.8.EE.C.8A