Systems Word Problems

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What is a system of linear equations?

Back

A set of two or more linear 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

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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 they reflect the problem's constraints.

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CCSS.HSA.CED.A.3

Front

What does it mean if two equations in a system are dependent?

Back

It means they represent the same line and have infinitely many solutions.

Tags

CCSS.8.EE.C.8B

Front

What does it mean if two equations in a system are independent?

Back

It means they represent different lines and have exactly one solution.

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CCSS.8.EE.C.8B

Front

What does it mean if two equations in a system are inconsistent?

Back

It means they represent parallel lines and have no solutions.

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CCSS.8.EE.C.8A

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

Back

Substitute the solution back into both equations to see if they hold true.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is the substitution method in solving systems of equations?

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A method where one equation is solved for one variable, and that expression is substituted 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

A method where equations are added or subtracted 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 do you interpret the solution of a system of equations in a real-world context?

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The solution represents the values of the variables that satisfy all conditions of the problem.

Tags

CCSS.8.EE.C.8B

Front

What is the significance of the coefficients in a system of equations?

Back

Coefficients represent the relationship between the variables in the equations, indicating how changes in one variable affect the other.

Tags

CCSS.8.EE.C.8B