Solving 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.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

What does it mean to solve a system of linear equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

What are the three possible outcomes when solving a system of linear equations?

Back

1. One solution (intersecting lines), 2. No solution (parallel lines), 3. Infinite solutions (coincident lines).

Tags

CCSS.8.EE.C.8B

Front

What is the elimination method?

Back

A technique for solving systems of equations by adding or subtracting equations to eliminate a variable.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

What is the substitution method?

Back

A technique for solving systems of equations by solving one equation for a variable and substituting that expression into the other equation.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

What does it mean if two lines are parallel in a system of equations?

Back

They have no points in common, meaning there is no solution to the system.

Tags

CCSS.8.EE.C.8B

Front

What does it mean if two lines are coincident?

Back

They lie on top of each other, meaning there are infinitely many solutions to the system.

Tags

CCSS.8.EE.C.8A

Front

How do you determine if a system of equations has one solution?

Back

If the lines represented by the equations intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

What is the first step in using the elimination method?

Back

Align the equations so that corresponding variables and constants are in the same columns.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

How can you check your solution to a system of equations?

Back

Substitute the solution back into the original equations to see if they hold true.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B