Elimination Method for Systems of Linear Equations

EXAMPLES

100

2x-3y=15

5x+3y=27

(6,-1)

200

5x+4y=-28

3x+10y=-13

(-6, 1/2)

300

9x-25y=-13

3x+10y=3

(-1/3, 2/5)

400

A business with two locations buys 7 large delivery vans and 5 small vans.  Location A receives 5 large vans and 2 samll vans for a total cost of $235000.  Location B receives 2 large vans and 3 small vans for a total cost of $160000.  What is the cost for a large and small van?

5x+2y=235000

2x+3y=160000

(Large $35000 and Small $30000)

Elimination #1

100

3x-y=14

5x+y=34

(6,4)

200

-x+6y=52

x+y=18

(8,10)

300

5x-2y=21

3x-y=21

(3,-3)

400

6x-3y=-63

2x+7y=19

(-8,5)

Elimination #2

100

4x+7y=-65

3x+2y=-26

(-4,-7)

200

10x-3y=-19

6x+5y=43

(1/2, 8)

300

8x-20y=-14

-12x-15y=3

(-3/4, 2/5)

400

9x+6y=8998

-11x+3000y=-12000

(1000,-1/3)

Elimination Word Problems

100

Mr Lube charges a fee for x dollars for an oil change PLUS y dollars per litre of oil used. The price is $22.45 for oil change if you have a 5 litre engine and $25.45 for a 7 litre engine.  Write a system of linear equations that represent this situation and find the fee and cost per litre for the oil.  

x+5y=22.45

x+7y-25.45

($14.98 - oil change fee,  $1.50 - per litre of oil)

200

A music website charges x dollars for individual songs and y dollars for entire albums.  Person A pays $25.92 to download 6 individual songs and 2 albums.  Person B pays $33.93 to downliad 4 individual songs and 3 albums.  Write a system of linear equations to determine what the website charges for an individual song and an entire album.  

6x+2y=25.92

4x+3y=33.93

Songs are $0.99 and Albums are $9.98

300

A rectangle has a perimeter of 18 inches.  A NEW rectangle has a perimeter of 46 if you TRIPLE the length and DOUBLE the width.  Write a system of linear equations and solve for the length and width of the orignial and new rectangles.  

2l+2w=18

6l+4w=46

(orig = 5" x 4" and NEW = 15" x 8")