Systems of Linear Equations

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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 two lines to be parallel in a system of linear equations?

Back

The lines have the same slope and will never intersect, meaning there is no solution.

Tags

CCSS.8.EE.C.8A

Front

What does it mean for two lines to be coincident in a system of linear equations?

Back

The lines are the same, resulting in infinite solutions.

Tags

CCSS.8.EE.C.8A

Front

What is the solution to a system of linear equations?

Back

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

Tags

CCSS.8.EE.C.8B

Front

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

Back

If the lines have different slopes, they will intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

What is the substitution method in solving systems of linear equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the elimination method in solving systems of linear equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean for two angles to be supplementary?

Back

The sum of the measures of the two angles is 180 degrees.

Tags

CCSS.7.G.B.5

Front

If x + y = 180 and y = 5x - 6, how can you find the values of x and y?

Back

Substitute y in the first equation to solve for x, then use that value to find y.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical representation of a system of linear equations?

Back

The lines representing each equation on a coordinate plane.

Tags

CCSS.8.EE.C.8A