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 if a system of equations has no solution?

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

Tags

CCSS.8.EE.C.8A

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How can you determine if a point is a solution to a system of equations?

Back

To determine if a point is a solution, substitute the x and y values of the point into each equation. If the point satisfies all equations, it is a solution.

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What is the substitution method for solving systems of equations?

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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 for 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

Front

What does it mean for a system of equations to have infinitely many solutions?

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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 do you graphically represent a system of equations?

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A system of equations can be represented graphically by plotting each equation on the same coordinate plane and identifying the points of intersection.

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CCSS.8.EE.C.8B

Front

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

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

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CCSS.8.EE.C.8B

Front

What is a consistent system of equations?

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

Tags

CCSS.8.EE.C.8B

Front

What is an inconsistent system of equations?

Back

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

Tags

CCSS.8.EE.C.8A