Systems of Equations: Choosing the Best Method

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What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the substitution method?

Back

A method for solving a system of equations by solving one equation for one variable and 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

A method for solving a system of equations by adding or subtracting equations to eliminate one variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphing method?

Back

A method for solving a system of equations by graphing the equations on the same coordinate plane and identifying the point(s) of intersection.

Tags

CCSS.8.EE.C.8B

Front

When is the graphing method most useful?

Back

When the equations are simple and can be easily graphed, or when a visual representation is needed.

Tags

CCSS.8.EE.C.8B

Front

When is the substitution method most useful?

Back

When one equation is easily solvable for one variable, making substitution straightforward.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

When is the elimination method most useful?

Back

When the coefficients of one variable are easily manipulated to eliminate that variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean if a system of equations has one solution?

Back

The lines representing the equations intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

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

Back

The lines representing the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A