Solving Systems of Equations

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What is a system of equations?

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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

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What does it mean to solve a system of equations graphically?

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Solving a system of equations graphically involves plotting the equations on a coordinate plane and identifying the point(s) where the lines intersect, which represents the solution(s) to the system.

Tags

CCSS.8.EE.C.8B

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What is the substitution method in solving systems of equations?

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The substitution method involves solving one of the equations for one variable and then substituting that expression into the other equation to find the values of the variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the elimination method in solving systems of equations?

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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

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What does it mean if two lines are parallel in a system of equations?

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If two lines are parallel, it means they have the same slope and will never intersect, indicating that the system has no solution.

Tags

CCSS.8.EE.C.8B

Front

What does it mean if two lines coincide in a system of equations?

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If two lines coincide, they lie on top of each other, indicating that there are infinitely many solutions to the system.

Tags

CCSS.8.EE.C.8A

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How can you determine the solution to a system of equations algebraically?

Back

To determine the solution algebraically, you can use either the substitution or elimination method to find the values of the variables that satisfy both equations.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the significance of the point of intersection in a system of equations?

Back

The point of intersection represents the solution to the system of equations, where the values of the variables satisfy all equations in the system.

Tags

CCSS.8.EE.C.8B

Front

What is a consistent system of equations?

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A consistent system of equations has at least one solution, which can be either a single point of intersection or infinitely many solutions.

Tags

CCSS.8.EE.C.8B

Front

What is an inconsistent system of equations?

Back

An inconsistent system of equations has no solutions, typically represented by parallel lines that do not intersect.

Tags

CCSS.8.EE.C.8A