Solving 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 simultaneously.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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

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The two main methods for solving systems of equations are substitution and elimination.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How does the substitution method work?

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

Front

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 remaining variable.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

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A consistent system of equations has at least one solution.

Tags

CCSS.8.EE.C.8B

Front

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

Back

An inconsistent system of equations has no solutions, meaning the lines represented by the equations do not intersect.

Tags

CCSS.8.EE.C.8B

Front

What is a dependent system of equations?

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

Tags

CCSS.8.EE.C.8B

Front

How can you determine if a system of equations has one solution, no solution, or infinitely many solutions?

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You can determine this by analyzing the slopes and intercepts of the lines represented by the equations. If the slopes are different, there is one solution; if the slopes are the same but intercepts differ, there is no solution; if both slopes and intercepts are the same, there are infinitely many solutions.

Tags

CCSS.8.EE.C.8B

Front

What is the first step in solving a system of equations by substitution?

Back

The first step is to solve one of the equations for one variable in terms of the other variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

When is it best to use the substitution method?

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The substitution method is best used when one equation is easily solvable for one variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6