System of Equations and Inequalities

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean for a point to be a solution to a system of equations?

Back

A point is a solution if it satisfies all equations in the system.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How can you solve a system of equations graphically?

Back

By plotting the equations on a graph and finding the intersection point(s).

Tags

CCSS.8.EE.C.8B

Front

What is 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 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 is an ordered pair?

Back

A pair of numbers (x, y) that represent a point on a coordinate plane.

Tags

CCSS.5.G.A.1

Front

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

Back

It means the lines represented by the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

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

Back

It means the equations represent the same line, so every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

Front

Solve the system of equations: 3x + y = 14 and y = x - 2.

Back

(4, 2)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

Solve the system of equations: 4x + 3y = 11 and -4x + y = 9.

Back

(-1, 5)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6