Checking solutions to linear systems

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What is a linear system?

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What does it mean for an ordered pair to be a solution to a linear system?

Back

An ordered pair is a solution to a linear system if it satisfies all equations in the system.

Front

How do you check if an ordered pair is a solution to a linear system?

Back

Substitute the x and y values of the ordered pair into each equation of the system. If all equations are true, it is a solution.

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What is the graphical representation of a linear system?

Back

The graphical representation of a linear system is the intersection point(s) of the lines represented by the equations.

Tags

CCSS.8.EE.C.8B

Front

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

Back

A linear system has no solution if the lines represented by the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

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

Back

A linear system has infinitely many solutions if the equations represent the same line, meaning they overlap completely.

Tags

CCSS.8.EE.C.8A

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What is the substitution method in solving linear systems?

Back

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 in solving linear systems?

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

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What is a consistent system of equations?

Back

A consistent system of equations has at least one solution.

Tags

CCSS.8.EE.C.8B

Front

What is an inconsistent system of equations?

Back

An inconsistent system of equations has no solutions.

Tags

CCSS.8.EE.C.8B