Solving Systems of Equations Warm Up

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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 set of values that satisfy all equations simultaneously.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean to solve a system of equations?

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To solve a system of equations means to find the values of the variables that make all equations in the system true.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What are the three main methods for solving systems of equations?

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The three main methods are Graphing, Substitution, and Elimination.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

When is graphing a suitable method for solving a system of equations?

Back

Graphing is suitable when the equations are simple and can be easily plotted on a graph to find the intersection point.

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CCSS.8.EE.C.8B

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What is the substitution method?

Back

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

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What is the elimination method?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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

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A system has no solution if the equations represent parallel lines that never intersect.

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CCSS.8.EE.C.8A

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

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A system has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.

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CCSS.8.EE.C.8A

Front

How do you determine if a system of equations is consistent or inconsistent?

Back

A consistent system has at least one solution, while an inconsistent system has no solutions.

Tags

CCSS.8.EE.C.8B

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Back

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6