Solutions System 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

Front

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

Back

The lines representing the equations intersect at exactly one point.

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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.

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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 representing the equations coincide, meaning they are the same line.

Tags

CCSS.8.EE.C.8A

Front

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

Back

By analyzing the intersection points of the graphed lines.

Tags

CCSS.8.EE.C.8B

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

Back

No solution, as the lines are parallel.

Tags

CCSS.8.EE.C.8B

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

Back

(1, 3), as the lines intersect at this point.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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

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What is a consistent system of equations?

Back

A system that has at least one solution.

Tags

CCSS.8.EE.C.8B