Writing Systems of Equations

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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 set of values that satisfy all equations in the system.

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 represent the same scenario.

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CCSS.HSA.CED.A.3

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What does the variable 'x' typically represent in a system of equations?

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In a system of equations, 'x' usually represents one of the unknown quantities that we are trying to solve for.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does the variable 'y' typically represent in a system of equations?

Back

In a system of equations, 'y' usually represents another unknown quantity that is related to 'x'.

Tags

CCSS.8.EE.C.8B

Front

What is the purpose of solving a system of equations?

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The purpose is to find the values of the variables that make all equations true simultaneously.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Front

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

Back

Substitute the values of the variables back into the original equations to see if they hold true.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

It means that the equations represent parallel lines that never intersect, indicating that there are no values that satisfy all equations.

Tags

CCSS.8.EE.C.8A

Front

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

Back

It means that the equations represent the same line, and any point on that line is a solution.

Tags

CCSS.8.EE.C.8A