Graphing and Substitution Systems

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.

Tags

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 are the same line.

Tags

CCSS.8.EE.C.8A

Front

What is the substitution method?

Back

A method for solving a system of equations by 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

Front

Solve the system by substitution: y = 3x + 2, y = -x + 4.

Back

(1, 5)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

Solve the system by substitution: 2x + y = 10, y = 3x - 2.

Back

(2, 6)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical representation of the equation y = mx + b?

Back

A straight line with slope m and y-intercept b.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How do you determine if two lines are parallel?

Back

If they have the same slope but different y-intercepts.

Tags

CCSS.8.EE.B.6

Front

How do you determine if two lines are perpendicular?

Back

If the product of their slopes is -1.

Tags

CCSS.8.EE.B.6