Systems of Equations Word Problems

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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.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

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

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CCSS.8.EE.C.8A

Front

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

Back

Identify the variables, write equations based on the relationships described in the problem, and ensure they represent the same situation.

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CCSS.HSA.CED.A.3

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression 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

The elimination method involves adding or subtracting 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

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 both equations are satisfied.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical method for solving systems of equations?

Back

The graphical method involves graphing both equations on the same coordinate plane and identifying the point of intersection.

Tags

CCSS.8.EE.C.8B

Front

What does it mean for two equations to be dependent?

Back

Dependent equations are equations that represent the same line, meaning they have infinitely many solutions.

Tags

CCSS.8.EE.C.8B

Front

What does it mean for two equations to be independent?

Back

Independent equations are equations that represent different lines, meaning they have exactly one solution.

Tags

CCSS.8.EE.C.8B

Front

How do you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and y-intercepts of the lines represented by the equations: parallel lines (no solution), same line (infinitely many solutions), or intersecting lines (one solution).

Tags

CCSS.8.EE.C.8B