System of Equations Word Problems

Front

Define a system of equations.

Back

A system of equations is a set of two or more equations with the same variables. The solution to the system is the set of values that satisfy all equations simultaneously.

Tags

CCSS.HSA.REI.C.8

Front

What is the graphical representation of a system of equations?

Back

The graphical representation of a system of equations is the point(s) where the graphs of the equations intersect. Each intersection point represents a solution to the system.

Tags

CCSS.8.EE.C.8B

Front

How do you solve a system of equations using substitution?

Back

To solve a system using substitution, solve one equation for one variable, then substitute that expression into the other equation to find the value of the second variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

Write a system of equations based on a word problem involving costs.

Back

Identify the variables, set up equations based on the relationships described in the problem, and ensure the equations reflect the total costs or quantities involved.

Tags

CCSS.HSA.CED.A.3

Front

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

Back

A consistent system of equations has at least one solution, meaning the equations intersect at one or more points.

Tags

CCSS.8.EE.C.8B

Front

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

Back

An inconsistent system of equations has no solution, meaning the equations represent parallel lines that never intersect.

Tags

CCSS.8.EE.C.8B

Front

What is a dependent system of equations?

Back

A dependent system of equations has infinitely many solutions, meaning the equations represent the same line.

Tags

CCSS.8.EE.C.8B

Front

How can you check the solution of a system of equations?

Back

To check the solution, substitute the values of the variables back into the original equations to verify that both equations are satisfied.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the importance of defining variables in word problems?

Back

Defining variables clearly helps to translate the problem into mathematical equations, making it easier to set up and solve the system.

Tags

CCSS.HSA.CED.A.3