Solving Systems of Equations #1
y= -3x+5
5x-4y= -3
x = 1, y = 2
-5x+y = -3
3x-8y= 24
x= 0, y= -3
A chemist mixed the contents of two jars. One of them contains a 32% solution of alcohol and the other contains an 80% solution of alcohol. He then has 100 cubic centimeters of a 64% solution of alcohol. How many cubic centimeters of the 32% solution did he start with?
33 1/3 cubic centimeters of 32% solution
-3x-3y=3
y= -5x-17
x= -4, y = 3
2x+y=20
6x-5y=12
x = 7, y = 6
The sum of the two digits of a number is 12. If the digits are reversed, the resulting number is 18 less than the original number. Find the original number.
75
-4x+y=6
-5x-y=21
x = -3, y = -6
3x-9y = -18
x = -6, y = 0
A collection of money consists of pennies, nickels, and dimes. There are 12 fewer dimes than nickels and 3 more pennies than nickels and the total value of the money is $10.35. Find how many coins there are in the collection.
207 coins
3+2x-y=0
-3-7y=10x
x= -1, y = 1
-14 = -20y-7x
10y+4=2x
x= 2, y = 0
If 2 machines work together on a job, they can do it in 1.8 days. The job can also be done if the first machine works for 2.5 days and the 2nd machine works for 0.75 of a day. How long would it take each machine working alone to do the job?
1st machine = 3 days, 2nd machine = 4.5 days