Systems 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

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

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Identify the variables, translate the relationships and conditions into equations, and ensure the equations 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 independent?

Back

Independent equations have different slopes and intersect at exactly one point, meaning there is one unique solution.

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CCSS.8.EE.C.8A

Front

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

Back

Dependent equations represent the same line, meaning there are infinitely many solutions.

Tags

CCSS.8.EE.C.8B

Front

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

Back

Inconsistent equations have no solutions because they represent parallel lines that never intersect.

Tags

CCSS.8.EE.C.8A

Front

How do you solve a system of equations using substitution?

Back

Solve one equation for one variable, then substitute that expression into the other equation to find the value of the second variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you solve a system of equations using elimination?

Back

Add or subtract the equations to eliminate one variable, making it easier to solve for the remaining variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the significance of the solution to a system of equations in a word problem?

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The solution represents the values of the variables that satisfy all equations, providing answers to the original problem.

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CCSS.8.EE.C.8C

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.

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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