System of Equations Word Problems

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

How do you represent a word problem as a system of equations?

Back

Identify the variables, translate the relationships and conditions into equations, and ensure the equations reflect the problem's constraints.

Tags

CCSS.HSA.CED.A.3

Front

What does the solution to a system of equations represent in a word problem?

Back

The solution represents the values of the variables that satisfy all equations in the system, often corresponding to real-world quantities.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

What is the substitution method for solving systems of equations?

Back

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

What is the elimination method for solving systems of equations?

Back

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

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

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

Back

Substitute the solution values back into the original equations to see if they satisfy all equations.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

What is the graphical method for solving systems of equations?

Back

The graphical method involves plotting the equations on a graph and identifying the point(s) where the lines intersect.

Tags

CCSS.8.EE.C.8B

Front

What is a consistent system of equations?

Back

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

Tags

CCSS.8.EE.C.8A

Front

What is an inconsistent system of equations?

Back

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

Tags

CCSS.8.EE.C.8A

Front

What is a dependent system of equations?

Back

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

Tags

CCSS.8.EE.C.8B