Solving Systems of Two 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

Parallel lines have no points in common; they do not intersect.

Tags

CCSS.8.EE.C.8A

Front

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

Back

Intersecting lines have exactly one point in common, which is the solution to the system.

Tags

CCSS.8.EE.C.8A

Front

What are coincident lines in a system of linear equations?

Back

Coincident lines are lines that lie on top of each other, representing an infinite number of solutions.

Tags

CCSS.8.EE.C.8A

Front

How do you solve a system of linear equations graphically?

Back

By plotting the equations on a graph and identifying the point(s) where they intersect.

Tags

CCSS.8.EE.C.8B

Front

What is the substitution method for 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 for 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

What is the solution to the system: y = 2/3x - 2 and y = -x + 3?

Back

(3, 0)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean if a system of equations has no solution?

Back

It means the lines are parallel and do not intersect.

Tags

CCSS.8.EE.C.8A

Front

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

Back

The point(s) where the lines representing the equations intersect.

Tags

CCSS.8.EE.C.8B