Solving Systems of Equations by Addition or Subtraction

Compare and contrast the substitution and elimination methods for solving a system of equations.

• Substitution method always leads to the correct solution, while elimination method is unreliable

• Substitution method involves adding the equations together, while elimination method involves multiplying the equations

• Both methods involve manipulating the equations to solve for one variable and then substituting or eliminating that variable to solve for the other variables.

• Substitution method only works for linear equations, while elimination method only works for quadratic equations

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

PAGE 135 #5: Here is a system of equations

-x+6y=9

x+6y=-3

Should you use subtraction or addition to solve the system?

• Addition to eliminate the x variable, then solve for y.

• Subtraction to eliminate the y variable, then solve for x.

• Both addition and subtraction would work depending on which variable you want to eliminate.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Here is a system of linear equations: 6x-y=18 4x+2y=26 Select ALL the steps that would help to eliminate a variable and enable solving.

• Multiply the first equation by 2, then subtract the second equation from the result.

• Multiply the first equation by 4, the second equation by 6, then subtract the resulting equations.

• Multiply the first equation by 2, then add the result to the second equation.

• Divide the second equation by 2, then add the result to the first equation.

• Multiply the second equation by 6, then subtract the result from the first equation.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

What is the x-value of the solution to the system?

(a)  

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

How many solutions does this system of equations have?

• One Solution

• Infinitely Many Solutions

• No Solution

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CCSS.8.EE.C.8B

PAGE 135: Solve each system of equations without graphing.

A.

2v+6w=-36

5v+2w=1

What is the w-value of the solution?

(a)  

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

PAGE 135 Solve each system of equations without graphing.

B.

6t-9u=10

2t+3u=4

What is the solution to the system?

• (4,-9)

• (-2,5)

• (11/6, 1,9)

• I don't know. I did not complete my workbook pages for homework.

• (1/2, 4/5)

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Used to solve a system of linear equations; one variable is removed by adding or subtracting the two equations of the system to obtain a single equation in one variable.

• Elimination Method

• Substitution Method

• Addition Property of Equality

• Additive Inverse

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

A set of two or more equations that contain two or more variables is called a (a)   .

• System of Equations

• Solution to a System of Equation

• Solution of an Equation

• Equation

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6