Systems of Equations--Substitution

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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 in the system.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is the substitution method in 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.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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How do you isolate a variable in an equation?

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To isolate a variable, you perform inverse operations to get the variable on one side of the equation by itself.

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CCSS.6.EE.B.7

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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 make all equations true 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 using the substitution method?

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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

Front

If you have the equations y = 2x + 3 and x + y = 10, how would you use substitution?

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Substitute y in the second equation: x + (2x + 3) = 10, then solve for x.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is the solution to the system of equations 2y + x = -15 and x = 3y?

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The solution is (-9, -3).

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What does it mean if two equations in a system have no solution?

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If two equations have no solution, it means they represent parallel lines that never intersect.

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CCSS.8.EE.C.8A

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What does it mean if two equations in a system have infinitely many solutions?

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If two equations have infinitely many solutions, it means they represent the same line, and every point on that line is a solution.

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CCSS.8.EE.C.8A

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

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You can check by substituting the solution back into the original equations to see if both equations are satisfied.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6