Systems of Equations

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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 infinitely many solutions?

Back

It means that the equations represent the same line, and every point on that line is a solution.

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CCSS.8.EE.C.8A

Front

How can you determine if a system of equations has no solution?

Back

If the equations represent parallel lines, they will never intersect, indicating no solution.

Tags

CCSS.8.EE.C.8A

Front

What is the graphical representation of a system of equations?

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The graphical representation consists of lines or curves plotted on a coordinate plane, where the intersection points represent the solutions.

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 that 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

Front

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

Back

A consistent system has at least one solution, which can be either unique or infinitely many.

Tags

CCSS.8.EE.C.8B

Front

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

Back

An inconsistent system has no solutions, typically represented by parallel lines.

Tags

CCSS.8.EE.C.8A

Front

How do you find the y-coordinate of the solution in a system of equations?

Back

You can substitute the x-coordinate into one of the original equations to find the corresponding y-coordinate.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the importance of isolating a variable in one equation?

Back

Isolating a variable makes it easier to use the substitution method to solve the system.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6