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 is the set of values that satisfy all equations simultaneously.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What does it mean to solve a system of equations by elimination?

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Solving by elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is substitution in the context of solving systems of equations?

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Substitution is a method where one equation is solved for one variable, and that expression is substituted into the other equation.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is the graphical interpretation of a system of equations?

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The solutions to a system of equations can be represented graphically as the points where the lines of the equations intersect.

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CCSS.8.EE.C.8B

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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 no points of intersection, indicating that the system has no solution.

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CCSS.8.EE.C.8A

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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.

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CCSS.8.EE.C.8A

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How do you check if a solution is correct for a system of equations?

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To check a solution, substitute the values back into the original equations to see if they hold true.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the first step in solving a system of equations by elimination?

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The first step is to align the equations and manipulate them to eliminate one variable, often by multiplying one or both equations.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the first step in solving a system of equations by substitution?

Back

The first step is to solve one of the equations for one variable in terms of the other variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

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Coefficients determine the slope and position of the lines represented by the equations, affecting their intersection.

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CCSS.8.EE.C.8A