Transcript 2.5
2-5 Systems of Equations Finding a solution that works for multiple equations Warm Up Please graph on one set of axes the following: x 2y 5 2x y 4 Solutions for multiple equations? That is, where 2 lines intersect. How can 2 lines intersect? One intersection No intersection Overlapping lines “Consistent” “Inconsistent” “Dependant” What methods have you already learned for finding where 2 line intersect? 1. Graphing Method - Don’t bother 2. Substitution Method Very good when one of the variables is already isolated 3. Addition/Subtraction Method More useful when isolating a variable (method 2) is messy. What method do you have to use? Unless specified (i.e. follow directions) you may use ANY method you want. I want you to be happy. Examples: 1. 3x 2y 7 xy 9 1 2 2. x y 1 2 3 x 6y 20 This doesn’t seem bad….. And it isn’t. Even when we apply this to word problems. Don’t get worried – these aren’t hard to set up. The only rule I have is this: for now, set up 2 equations with 2 unknowns. I am WELL AWARE that there will be other methods, but I am checking your ability to set up 2 equation/2 unknown problems and then solve them. Examples 1. A golfer scored only 4’s and 5’s in a round of 18 holes. His score was 80. How many of each score did he have? 2. Eight less than four times a number is three more than five times another number. Together the numbers total 16. What are the numbers? 3. Tuition plus Room/Board at a local college is $24,000. Room/Board is $400 more than one-third the tuition. Find the tuition. Examples 4. Mr. Trem bought 7 shirts for the coaches of his baseball team. The blue long sleeved shirts cost $30 each and the white short sleeved shorts cost $20 each. If he paid a total of $160, how many of each shirt did he buy?? 5. Rob invests money, some at 10% and some at 20% earning $20 in interest per year. Had the amounts invested been reversed, he would have received $25 in interest. How much has he invested all together? Examples 6. A merchant said that it did not matter whether one pair of shoes was sold for $31 or two pairs for $49 because the profit was the same for each sale. How much does one pair of shoes cost the merchant and what is the profit?? 7. The sum of two numbers is 20. The larger is 5 less than twice the smaller. What are the numbers??