Systems of Equations - Word Problems & More

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What is a system of equations?

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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.

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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 they reflect the problem's context.

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CCSS.HSA.CED.A.3

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What does it mean for two equations to be equivalent?

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Two equations are equivalent if they have the same solution set, meaning they represent the same line when graphed.

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CCSS.8.EE.C.7A

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What is the substitution method in solving systems of equations?

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The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is the elimination method in solving systems of equations?

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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

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

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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

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What is a consistent system of equations?

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A consistent system has at least one solution, meaning the lines intersect at one or more points.

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CCSS.8.EE.C.8A

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What is an inconsistent system of equations?

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An inconsistent system has no solutions, meaning the lines are parallel and never intersect.

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CCSS.8.EE.C.8A

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What is a dependent system of equations?

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A dependent system has infinitely many solutions, meaning the equations represent the same line.

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CCSS.8.EE.C.8B

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How do you interpret the solution of a system of equations in a word problem?

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The solution represents the values of the variables that satisfy all conditions of the problem, often corresponding to real-world quantities.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6