Solving Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean if two lines are parallel when graphing a system of equations?

Back

It means there is no solution to the system because the lines never intersect.

Tags

CCSS.8.EE.C.8B

Front

What does it mean if two lines coincide when graphing a system of equations?

Back

It means there are infinite solutions to the system because the lines are the same.

Tags

CCSS.8.EE.C.8A

Front

How can you eliminate a variable in a system of equations?

Back

By adding or subtracting the equations after multiplying them by appropriate coefficients.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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

Solve for x and y: 2x + 3y = 6, x - y = 1

Back

(3,0)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

Solve for x and y: 4x - y = 7, 2x + 3y = 12

Back

(3,2)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

The point where the lines representing the equations intersect.

Tags

CCSS.8.EE.C.8A

Front

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

Back

The lines intersect at a single point, indicating a unique solution for the variables.

Tags

CCSS.8.EE.C.8A