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 solve a system of equations using substitution?

Back

To solve by substitution, solve one equation for one variable, then substitute that expression into the other equation.

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CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

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.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

What does it mean for a system of equations to be consistent?

Back

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

Tags

CCSS.8.EE.C.8B

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system has no solutions, meaning the equations represent parallel lines that never intersect.

Tags

CCSS.8.EE.C.8A

Front

What is a dependent system of equations?

Back

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

Tags

CCSS.8.EE.C.8B

Front

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

Back

Identify the variables, translate the relationships and conditions into equations, and set them up as a system.

Tags

CCSS.HSA.CED.A.3

Front

What is the first step in solving a word problem involving a system of equations?

Back

The first step is to define the variables that represent the unknown quantities in the problem.

Tags

CCSS.8.EE.C.8C

Front

How do 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 the importance of units in word problems?

Back

Units help ensure that the quantities being compared or calculated are consistent, which is crucial for accurate solutions.

Tags

CCSS.8.EE.C.7B