Systems of Linear Equations

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean for a point to be a solution to a system of equations?

Back

It means that the point satisfies all equations in the system.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How can you determine if (4, 1) is a solution for the system of equations: y = -x + 5 and y = 2x - 7?

Back

Substitute x=4 and y=1 into both equations. Both should hold true.

Front

What are the three main methods to solve systems of equations?

Back

Graphing, Substitution, Elimination.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean if two lines on a graph are parallel?

Back

They have no solutions because they never intersect.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if two lines on a graph are the same line?

Back

They have infinite solutions because every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

Front

How do you solve a system of equations using the substitution method?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you solve a system of equations using the elimination method?

Back

Add or subtract the equations to eliminate one variable, then solve for the other.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the lines represent the solutions.

Tags

CCSS.8.EE.C.8A

Front

If a system of equations has no solution, what does that indicate about the lines?

Back

The lines are parallel and will never intersect.

Tags

CCSS.8.EE.C.8A