Graphing 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 to solve a system of equations by graphing?

Back

It means to find the point(s) where the graphs of the equations intersect.

Tags

CCSS.8.EE.C.8B

Front

What is the solution to a system of equations?

Back

The point(s) where the equations intersect, representing the values of the variables that satisfy all equations.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

The graphs of the equations intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

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

Back

The graphs of the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

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

Back

The graphs of the equations are the same line, meaning every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

Front

How can 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

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 find the slope of a line given two points?

Back

Use the formula m = (y2 - y1) / (x2 - x1).

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept of the equation y = 1/2x + 2?

Back

The y-intercept is 2.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3