systems+and+word+problems+day+1

Section 7.4 (continued) 1.) Define 2 different variables. 2.) Set up 2 different equations based upon information in the problem. 3.) Solve.
 * __Using systems to solve word problems__**

Ex: Solve The sum of 2 numbers is 64 and their differences is 36. What are the numbers? x=1st number y=2nd number x+y=64 x-y=36 cancel out the y variable because one is negative and one is positive. 2x=100 x=50

Plug the answer into one of the equations. x+y=64 50+y=64 y=14

Ex: I am looking for 2 unknown numbers whose difference is 3. 4 times the larger number plus twice the smaller is 60. What are the numbers. x= larger number y= smaller number x-y=3--->2x-2y=6 4x+2y=60--->4x+2y=60 multiply the first equation by 2 so x turns to y becomes -2y and the cancel out. 66x=66 x=11

Plug the answer into one of the equations. 4x+2y=60 44+2y=60 Subtract 44 from both sides 2y=16 Divide both sides by 2. y=8