number of solutions to a system 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 if a system of equations has no solution?

Back

It means the lines represented by the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

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

Back

It means the lines intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

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

Back

It means the equations represent the same line, so every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

Front

How can you determine the number of solutions to a system of equations graphically?

Back

By graphing the equations and observing the points of intersection.

Tags

CCSS.8.EE.C.8B

Front

What is the significance of the slopes of two lines in a system of equations?

Back

If the slopes are equal and the y-intercepts are different, there are no solutions. If the slopes are different, there is one solution. If the slopes and y-intercepts are the same, there are infinitely many solutions.

Tags

CCSS.8.EE.C.8B

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

If two equations are identical, how many solutions does the system have?

Back

Infinitely many solutions.

Tags

CCSS.8.EE.C.8B

Front

What is the graphical representation of the equations y = 3x - 1 and y = 3x - 1?

Back

They represent the same line, indicating infinitely many solutions.

Tags

CCSS.8.EE.C.8A

Front

What is the graphical representation of the equations y = 4x + 2 and y = 4x + 2.01?

Back

They are parallel lines, indicating no solutions.

Tags

CCSS.8.EE.C.8B