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 reflect the problem's context.

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CCSS.HSA.CED.A.3

Front

What does it mean to solve a system of equations?

Back

To find the values of the variables that satisfy all equations in the system simultaneously.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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

What is a linear equation?

Back

A linear equation is an equation that forms a straight line when graphed, typically in the form y = mx + b.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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What does it mean for two equations to be equivalent?

Back

Two equations are equivalent if they have the same solution set, meaning they intersect at the same point(s) on a graph.

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CCSS.8.EE.C.7A

Front

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

Back

Substitute the solution 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 a word problem?

Back

A word problem is a mathematical problem presented in a narrative form, requiring interpretation and translation into mathematical expressions.

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CCSS.HSA-SSE.A.1A

Front

What is the importance of defining variables in word problems?

Back

Defining variables helps clarify what each symbol represents, making it easier to set up equations and solve the problem.

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CCSS.6.EE.B.6