System of Equations Word Problems

Front

What is a system of equations?

Back

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

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 the lines represented by the equations intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

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

Back

It means the lines represented by the equations are the same line, overlapping each other.

Tags

CCSS.8.EE.C.8A

Front

How do you solve a system of equations by substitution?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you solve a system of equations by elimination?

Back

Add or subtract the equations 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 graphical representation of a system of equations?

Back

It is represented by lines on a coordinate plane, where the intersection points represent the solutions.

Tags

CCSS.8.EE.C.8A

Front

What is the first step in solving a word problem involving a system of equations?

Back

Identify the variables and what they represent in the context of the problem.

Tags

CCSS.8.EE.C.8C

Front

What is the importance of defining the variables in a word problem?

Back

Defining the variables helps to translate the problem into mathematical equations.

Tags

CCSS.6.EE.B.6

Front

How can you check if your solution to a system of equations is correct?

Back

Substitute the solution back into the original equations to see if they hold true.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6