Systems Substitution Method

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What is the substitution method in solving systems of equations?

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The substitution method is a technique used to solve systems of equations by 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

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What does it mean for an equation to be 'solved'?

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An equation is considered 'solved' when it has been manipulated to express one variable in terms of the other variables, allowing for substitution.

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How do you identify a solved equation in a system?

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A solved equation will have one variable isolated on one side of the equation, making it easy to substitute into another equation.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is the first step in the substitution method?

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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If you have the equations y = 2x + 3 and 3x + 2y = 12, how would you use substitution?

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Substitute y from the first equation into the second equation: 3x + 2(2x + 3) = 12.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is the solution to the system of equations y = 2x + 3 and 3x + 2y = 12?

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The solution is (2, 7), found by solving the equations using substitution.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is a key advantage of the substitution method?

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A key advantage is that it can simplify the process of solving systems, especially when one equation is already solved for a variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What should you do if both equations in a system are not easily solvable for one variable?

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You may need to manipulate one or both equations to isolate a variable before using substitution.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is the importance of checking your solution after using the substitution method?

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Checking your solution ensures that the values satisfy both original equations, confirming that the solution is correct.

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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It means that the lines represented by the equations are parallel and do not intersect.

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CCSS.8.EE.C.8A