Solving Systems

Front

What is a system of equations?

Back

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

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

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 one solution?

Back

The lines intersect at exactly one point, representing a unique solution.

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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 lines coincide, meaning they are the same line and have an infinite number of intersection points.

Tags

CCSS.8.EE.C.8A

Front

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

Back

By analyzing the intersection points of the lines on a graph.

Tags

CCSS.8.EE.C.8B

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is 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, making it easier to solve for the other.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

What is the graphical method of solving systems of equations?

Back

Plotting the equations on a graph and identifying the points of intersection.

Tags

CCSS.8.EE.C.8B

Front

What is the solution to the system: -4x - 2y = -12 and 4x + 8y = -24?

Back

(6, -6)

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CCSS.HSA.REI.C.9

Front

What is the solution to the system: 2x + 3y = 6 and 4x + 6y = 12?

Back

Infinitely many solutions.

Tags

CCSS.8.EE.C.8B