Solving Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

The lines representing the equations are parallel and never intersect.

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CCSS.8.EE.C.8A

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

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CCSS.8.EE.C.8A

Front

How can you determine the number of solutions in a system of equations?

Back

By graphing the equations and observing the intersection points.

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CCSS.8.EE.C.8B

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What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and then substituted into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical method for solving systems of equations?

Back

Plotting the equations on a graph and finding the intersection point.

Tags

CCSS.8.EE.C.8B

Front

If a system of equations is represented by y = mx + b, what do m and b represent?

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m is the slope of the line, and b is the y-intercept.

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CCSS.8.F.A.3

CCSS.8.EE.B.6

Front

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

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They determine the slope and position of the lines on a graph.

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CCSS.8.EE.C.8A

Front

How do you represent a system of equations algebraically?

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By writing two or more equations that share the same variables.

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CCSS.HSA.REI.C.8