Solving Systems of Two 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 system of equations to have one solution?

Back

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

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CCSS.8.EE.C.8A

Front

What does it mean for a system of equations to have no solutions?

Back

The lines represented by the equations are parallel and never intersect.

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CCSS.8.EE.C.8A

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

The lines represented by the equations coincide, meaning they are the same line.

Tags

CCSS.8.EE.C.8A

Front

How can you determine if two lines intersect?

Back

By solving the system of equations to find a common solution (x, 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

It is represented by lines on a coordinate plane.

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 then 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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

y = mx + b, where m is the slope and b is the y-intercept.

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CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What is the point of intersection of two lines?

Back

The point (x, y) that satisfies both equations in the system.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6