Systems of Equations

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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 to the system is the set of values that satisfy all equations simultaneously.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean to solve a system of equations?

Back

To solve a system of equations means to find the values of the variables that make all equations in the system true at the same time.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What are the three methods for solving systems of equations?

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The three methods are: 1) Graphing, 2) Substitution, 3) Elimination.

Tags

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 remaining variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean if a system of equations has no solution?

Back

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

Tags

CCSS.8.EE.C.8A

Front

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

Back

A system has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

Front

How can you determine if a system of equations is consistent or inconsistent?

Back

A system is consistent if it has at least one solution; it is inconsistent if it has no solutions.

Tags

CCSS.8.EE.C.8B

Front

What is the graphical representation of a system of equations?

Back

The graphical representation involves plotting each equation on a coordinate plane and identifying the point(s) of intersection.

Tags

CCSS.8.EE.C.8B

Front

What is the role of coefficients in a system of equations?

Back

Coefficients determine the slope and position of the lines represented by the equations in a system.

Tags

CCSS.8.EE.C.8A