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 for a system of equations to have a unique solution?

Back

It means there is exactly one set of values for the variables that satisfies all equations in the system.

Tags

CCSS.8.EE.C.8B

Front

What is the graphical representation of a system of equations?

Back

The graphs of the equations plotted on the same coordinate plane.

Tags

CCSS.8.EE.C.8B

Front

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

Back

They have the same slope and will never intersect, indicating no solution.

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

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

Back

It means that the equations represent the same line, and there are countless points that satisfy both equations.

Tags

CCSS.8.EE.C.8B

Front

How can you determine if a system of equations has no solution?

Back

If the equations represent parallel lines, they will never intersect, indicating no solution.

Tags

CCSS.8.EE.C.8A

Front

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

Back

(3,0) is the solution.

Tags

CCSS.HSA.REI.C.9

Front

Solve for x and y: y = 4x + 1 and y = -2x + 5.

Back

(1,5) is the solution.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6