8.9a Solutions to systems

Front

What is a solution to a system of equations?

Back

A solution to a system of equations is a set of values for the variables that makes all the equations true simultaneously.

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 that the equations represent parallel lines that never intersect.

Tags

CCSS.8.EE.C.8A

Front

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

Back

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

Tags

CCSS.8.EE.C.8A

Front

How do you find the solution to a system of equations graphically?

Back

You graph both equations on the same coordinate plane and identify the point where they intersect.

Tags

CCSS.8.EE.C.8B

Front

What is the solution to the system of equations: y = 2x + 1 and y = -x + 4?

Back

(1, 3)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical representation of a system with one solution?

Back

Two lines that intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

What is the graphical representation of a system with no solution?

Back

Two parallel lines that never meet.

Tags

CCSS.8.EE.C.8A

Front

What is the graphical representation of a system with infinitely many solutions?

Back

Two lines that lie on top of each other.

Tags

CCSS.8.EE.C.8A

Front

If the equations are y = 3x + 2 and y = 3x - 1, how many solutions does this system have?

Back

No Solution.

Tags

CCSS.8.EE.C.8B

Front

What is the first step in solving a system of equations by substitution?

Back

Solve one of the equations for one variable in terms of the other.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6