Systems of Equations And Inequalities

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What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean to solve a system of equations?

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To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What are the three methods to solve a system of equations?

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1. Graphing 2. Substitution 3. Elimination

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the substitution method?

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 other.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is an inconsistent system of equations?

Back

An inconsistent system of equations is one that has no solution, meaning the lines represented by the equations are parallel.

Tags

CCSS.8.EE.C.8A

Front

What is a consistent system of equations?

Back

A consistent system of equations has at least one solution, which can be either one unique solution or infinitely many solutions.

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CCSS.8.EE.C.8B

Front

What is a dependent system of equations?

Back

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

Tags

CCSS.8.EE.C.8B

Front

How do you graph a system of equations?

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To graph a system of equations, plot each equation on the same coordinate plane and identify the point(s) where they intersect.

Tags

CCSS.8.EE.C.8B

Front

What is the graphical interpretation of a solution to a system of equations?

Back

The solution to a system of equations is represented by the point(s) where the graphs of the equations intersect.

Tags

CCSS.8.EE.C.8B