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.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

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

Back

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

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CCSS.8.EE.C.8A

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What does it mean if a system of equations has infinitely many solutions?

Back

It means the equations represent the same line, so every point on the line is a solution.

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CCSS.8.EE.C.8A

Front

What is the elimination method?

Back

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

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the substitution method?

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 graphing method?

Back

The graphing method involves graphing each equation on the same coordinate plane to find the point(s) of intersection.

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CCSS.8.EE.C.8B

Front

What is the meaning of the variables in a system of equations?

Back

Variables represent unknown quantities that we are trying to solve for in the equations.

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CCSS.8.EE.C.8B

Front

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

Back

You can substitute the solution back into the original equations to see if both equations are satisfied.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

What is a word problem in the context of systems of equations?

Back

A word problem is a real-life scenario that can be modeled using a system of equations to find unknown values.

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CCSS.8.EE.C.8C

Front

How do you translate a word problem into 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.8.EE.C.8C