A.3F Algebra Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

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?

Back

The lines representing the equations are parallel and never intersect.

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CCSS.8.EE.C.8A

Front

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

Back

The lines intersect at exactly one point, which is the solution.

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CCSS.8.EE.C.8A

Front

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

Back

The lines coincide, meaning they are the same line.

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CCSS.8.EE.C.8A

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How can you determine the number of solutions in a system of equations?

Back

By graphing the equations and observing their intersection points.

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CCSS.8.EE.C.8B

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What is the solution to the system of equations: y = 2x + 1 and y = -x + 4?

Back

(1, 3)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the solution to the system of equations: 2x + 3y = 6 and x - y = 1?

Back

(3, 0)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical representation of a system of equations?

Back

It is represented by lines on a coordinate plane.

Tags

CCSS.8.EE.C.8A

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and then substituted 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?

Back

A method where equations are added or subtracted to eliminate one variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6