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

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 represent the same scenario.

Tags

CCSS.HSA.CED.A.3

Front

What does the term 'solution' mean in the context of a system of equations?

Back

The solution is the set of values for the variables that satisfy all equations in the system.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the substitution method for 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 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.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 values of the variables back into the original equations to see if they hold true.

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 the equations represent parallel lines that 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, and there are countless points of intersection.

Tags

CCSS.8.EE.C.8A

Front

How do you set up a system of equations from a word problem involving money?

Back

Define variables for the amounts involved, create equations based on the total amounts and relationships given in the problem.

Tags

CCSS.8.EE.C.8C

Front

What is the first step in solving a word problem involving ages?

Back

Define variables for the ages of the individuals involved and set up equations based on the relationships described.

Tags

CCSS.8.EE.C.7B