Substitution systems

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What is a substitution system in mathematics?

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A substitution system is a method used to solve systems of equations by substituting one equation into another to find the values of the variables.

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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?

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To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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

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

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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The solution is (2, 3).

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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 graphical interpretation is that each equation represents a line, and the solution is the point(s) where the lines intersect.

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CCSS.8.EE.C.8B

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What does it mean if a system of equations has no solution?

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It means that the lines represented by the equations are parallel and never intersect.

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CCSS.8.EE.C.8A

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What does it mean if a system of equations has infinite solutions?

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It means that the equations represent the same line, and there are an infinite number of points that satisfy both equations.

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CCSS.8.EE.C.8A

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

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You can check by substituting 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

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What is the substitution method?

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The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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The solution is (3, 0).

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CCSS.HSA.REI.C.9