Solving 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 if a system of linear equations has no solution?

Back

The lines representing the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if a system of linear equations has one solution?

Back

The lines intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if a system of linear equations has infinitely many solutions?

Back

The lines are the same, meaning they overlap completely.

Tags

CCSS.8.EE.C.8A

Front

What is the elimination method for solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate one variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the substitution method for solving systems of equations?

Back

A method where one equation is solved for one variable, which is then substituted into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and intercepts of the lines represented by the equations.

Tags

CCSS.8.EE.C.8B

Front

What is the graphical representation of a system of equations?

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The graph shows the lines of the equations, and their intersections represent the solutions.

Tags

CCSS.8.EE.C.8A

Front

Solve by elimination: 2x + 3y = 6 and 4x - 3y = 12.

Back

(3,0)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

Solve by substitution: y = 2x + 3 and 3x - y = 5.

Back

(1,5)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6