Systems of equations and inequalities

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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 for a system of equations to have a unique solution?

Back

It means there is exactly one set of values for the variables that satisfies all equations in the system.

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CCSS.8.EE.C.8B

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What is an inconsistent system of equations?

Back

A system that has no solution because the equations represent parallel lines.

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CCSS.8.EE.C.8A

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What is a dependent system of equations?

Back

A system that has infinitely many solutions because the equations represent the same line.

Tags

CCSS.8.EE.C.8B

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How do you solve a system of equations using substitution?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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How do you solve a system of equations using elimination?

Back

Add or subtract the equations to eliminate one variable, making it easier to solve for the other.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical representation of a system of equations?

Back

The solution is the point(s) where the graphs of the equations intersect.

Tags

CCSS.8.EE.C.8B

Front

What is a system of inequalities?

Back

A set of two or more inequalities that are solved together.

Tags

CCSS.8.EE.C.8B

Front

How do you graph a linear inequality?

Back

Graph the corresponding equation as a line, then shade the region that satisfies the inequality.

Tags

CCSS.HSA.REI.D.12

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

Back

It means that the point satisfies all equations in the system.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6