Solving Linear Systems & Inequalities

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What is a linear system?

Back

A linear system is a collection of one or more linear equations involving the same variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What are the two main methods for solving linear systems?

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The two main methods for solving linear systems are elimination and substitution.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean if a linear system has no solution?

Back

A linear system has no solution if the equations represent parallel lines that never intersect.

Tags

CCSS.8.EE.C.8A

Front

What is the graphical representation of a solution to a linear equation?

Back

The graphical representation of a solution to a linear equation is the point where the line intersects the coordinate plane.

Tags

CCSS.8.EE.C.8A

Front

How do you determine if a point is a solution to a system of inequalities?

Back

A point is a solution to a system of inequalities if it satisfies all the inequalities in the system.

Front

What is the significance of the shaded region in a graph of inequalities?

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The shaded region in a graph of inequalities represents all the possible solutions that satisfy the inequality.

Tags

CCSS.HSA.REI.D.12

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

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A system of equations is consistent if it has at least one solution.

Tags

CCSS.8.EE.C.8B

Front

What is the difference between a consistent and an inconsistent system?

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A consistent system has at least one solution, while an inconsistent system has no solutions.

Tags

CCSS.8.EE.C.8B

Front

What is the substitution method for solving linear equations?

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The substitution method involves 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 for solving linear equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6