EXAMPLES
2x-3y=15
5x+3y=27
(6,-1)
3x-y=14
5x+y=34
(6,4)
4x+7y=-65
3x+2y=-26
(-4,-7)
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)
5x+4y=-28
3x+10y=-13
(-6, 1/2)
-x+6y=52
x+y=18
(8,10)
10x-3y=-19
6x+5y=43
(1/2, 8)
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
9x-25y=-13
3x+10y=3
(-1/3, 2/5)
5x-2y=21
3x-y=21
(3,-3)
8x-20y=-14
-12x-15y=3
(-3/4, 2/5)
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")
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)
6x-3y=-63
2x+7y=19
(-8,5)
9x+6y=8998
-11x+3000y=-12000
(1000,-1/3)