SLIDE SHOW

Solve the linear system using the substitution method.

3 x + 4y – 4 Equation 1

x + 2y 2 Equation 2

x + 2y 2

x – 2y + 2

3(– 2y + 2) + 4y – 4

y 5

SOLUTION

-6y+6+4y – 4-2y = -10

x – 2y + 2

x – 2(5) + 2

x – 8

The solution is (– 8, 5).

1.

x – 2 y 32 x – 4 y 7

2(2 y + 3) – 4 y 76 7

Because the statement 6 = 7 is never true, there is no solution.

2.

Solve the linear system using the substitution method.

x 2 y + 3

Solve the linear system using thelinear combination/elimination method. 2 x – 4y 13 Equation 1

4 x – 5y 8 Equation 2

– 4x + 8y – 26

4 x – 5y 8

2 x – 4y 13

4 x – 5y 8

3y –18

y – 6

Multiply the first equation by – 2 so that x-coefficients differ only in sign.

SOLUTION

• – 2

3.

The Linear Combination Method: Multiplying One Equation

2 x – 4y 13

2 x – 4(– 6) 13

2 x + 24 13

x –11

2

The solution is – , – 6 .(-51

2 )

y – 6Add the revised equations and solve for y.

Write Equation 1.

Substitute – 6 for y.

Simplify.

Solve for x.

Substitute the value of y into one of the original equations.

Solve the linear system using thelinear combination method.

2 x – 4y 13 Equation 1

4 x – 5y 8 Equation 2

6 x – 10 y 12 – 15 x + 25 y – 30

Solve the linear system

6 x – 10 y 12

– 15 x + 25 y – 30

30 x – 50 y 60

– 30 x + 50 y – 60

0 0Add the revised equations.

Since no coefficient is 1 or –1, use the linear combination method.

Because the equation 0 = 0 is always true, there are infinitely many solutions.

SOLUTION

• 5

• 2

4.

7 x – 12 y – 22 Equation 1

– 5 x + 8 y 14 Equation 2

Solve the linear system using thelinear combination method.

7 x – 12 y – 22

– 5 x + 8 y 14

14 x – 24y – 44

– 15 x + 24y 42

Add the revised equations and solve for x.

– x – 2

x 2

Multiply the first equation by 2 and the second equation by 3 so that the coefficients of y differ only in sign.

SOLUTION

• 2

• 3

5.

– 5 x + 8 y 14

y = 3

– 5 (2) + 8 y 14

The solution is (2, 3).

x 2Add the revised equations and solve for x.

Write Equation 2.

Substitute 2 for x.

Solve for y.

Substitute the value of x into one of the original equations. Solve for y.

7 x – 12 y – 22 Equation 1

– 5 x + 8 y 14 Equation 2

Solve the linear system using thelinear combination method.

Check the solution algebraically or graphically.

6. If Brian bought 6 markers and 12 pens for $21.60 and then had to go back and buy 18 more markers and 20 pens for $50.40. How much was each item?

7. If Maria bought 33 books notebooks for $393. Each book costs $23.50 and each notebook costs $2.25. How many of each did she purchase?

6x + 12y = 21.60

18x + 20y = 50.40

x = 1.8y = .9Markers costs $1.80

Pens costs $0.90

x + y = 33

23.5x + 2.25y = 393

x = 15y = 18

15 Books

18 Notebooks

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