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

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

Back

A system is consistent if it has at least one solution.

Tags

CCSS.8.EE.C.8B

Front

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

Back

A system is inconsistent if it has no solutions.

Tags

CCSS.8.EE.C.8B

Front

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

Back

The point where the lines intersect on a graph.

Tags

CCSS.8.EE.C.8A

Front

What is the substitution method in solving systems of 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 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

How do you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into both equations; if both equations are true, the point is a solution.

Front

What is the slope-intercept form of a linear equation?

Back

The form is 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

What is the meaning of the slope in a linear equation?

Back

The slope represents the rate of change of y with respect to x.

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x = 0.