What if both of the variables cancel out?

Size: px

Start display at page:

Download "What if both of the variables cancel out?"

Kathleen McBride
6 years ago
Views:

1 Name:. Solving Sstems of Equations Algebraicall Lesson Essential Question: How do ou solve a sstem of equations algebraicall? SUBSTITUTION ELIMINATION Definition- Definition- - = -6 + = - - = -6 + = - When a sstem of equations have one solution, the solution is written as an. What if both of the variables cancel out? * False statement indicates the lines are parallel so there is. * True statement indicates the lines coincide so there are. 1

2 How do ou solve a sstem of equations b using substitution? Eample 1: + = 4 = 1. Choose one equation and solve for or. Eample : + = 1 = Choose one equation and solve for or.. Substitute the epression from that equation in to the other equation.. Substitute the epression from that equation in to the other equation.. Solve for the variable.. Solve for the variable. 4. Substitute the value found in step () back into the equation solved in step one. 4. Substitute the value found in step () back into the equation solved in step one. 5. Test our solution (,) into one of the original equations. 5. Test our solution (,) into one of the original equations.

3 Eample : + = 5 = 4 1. Choose one equation and solve for or. Eample 4: + = = - 1. Choose one equation and solve for or.. Substitute the epression from that equation in to the other equation.. Substitute the epression from that equation in to the other equation.. Solve for the variable.. Solve for the variable. 4. Substitute the value found in step () back into the equation solved in step one. 4. Substitute the value found in step () back into the equation solved in step one. 5. Test our solution (,) into one of the original equations. 5. Test our solution (,) into one of the original equations.

4 4 Solve each sstem b substitution: d c d c

5 Elimination Steps: 1... Eamples: Solve the sstem of equation using elimination a. b. c. d. You Tr: Solve the sstem of equation using elimination a. b. c. d. 5

6 Elimination Practice (with multiplication) Steps: 1. Multipl each equation b a number that will cause one variable to cancel out. Add both equations to eliminate a variable and solve for one variable. Substitute the value from step into either equation to solve for the other variable 4. Write solution as an ordered pair m n 8 4m n

7 Name: Date: Period: 4 Step Method 1. Define Variables. Write the sstems of equations.. Solve showing all steps. 4. State our solution in sentence form. 1) You sell tickets for admissions to our school pla and collect a total of $104. Admission prices are $6 for adults and $4 for children. You sold 1 tickets. How man tickets and how man children tickets did ou sell? ) Your famil goes to a restaurant for dinner. There are 6 people in our famil. Some order the chicken dinner for $14.80 and some order steak for $17. If the total bill was $91, how man people order each tpe of dinner? ) You bought the meat for Saturda s cookout. A package of hot dogs cost $1.60 and a package of hamburger cost $5. You bought a total of 8 packages of meat and spent $. How man packages of hamburger meat did ou bu? 4) Case orders pizzas and orders of breadsticks for a total of $9.50. Rachel orders pizzas and orders of breadsticks for a total of $. How much does the pizza cost? 5) Rent A Car rents compact cars for a fied amount per da plus a fied amount for each mile driven. Benito rented a car for 6 das, drove it 550 miles and spent $7. Lisa rented the same car for das, drove it 50 miles, and spent $185. What are the charges per da and per mile for the compact car? 6) Beach Hotel in Cancun is offering two weekend specials. One includes a -night sta with meals and costs $195. The other includes a -night sta with 5 meals and costs $00. What is the cost of a single meal? 7

8 7) You and our friend go to a Meican restaurant. You order tacos and enchiladas. Your friend orders tacos and 1 enchilada. Your bill was $4.80. Your friend s bill was $4.00. What was the price of an enchilada? 8) For a communit bake sale, ou purchase 1 pounds of sugar and 15 pounds of flour. Your total cost was $9.0. The net da, ou purchased 4 pounds of sugar and 10 pounds of flour. Your total cost the second da was $4.60. Find the cost of a pound of sugar and a pound of flour. 9) A travel agenc offers different gatewas to New York. Plan A includes hotel accommodations for -nights and -pair of baseball tickets for $645. Plan B includes hotel accommodations for 5-nights and 4-pairs of baseball tickets for $115. How much does a one-night hotel cost and how much does a single pair of baseball tickets cost? 10) Tickets for the theater are $5 for the balcon and $10 for the orchestra. If 600 tickets were sold and the total came to $4750, how man tickets of each tpe were sold? 11) You bought 5 pairs of socks for $19. The wools socks that ou bought cost $5 per pair. The cotton socks ou bought cost $ per pair. How man of each tpe of sock did ou bu? 1) A sporting goods store sells right-handed and left-handed baseball gloves. In one month, 1 gloves were sold for total revenue of $58. Right-handed gloves cost$48 and left-handed gloves costs $6. How man right-handed gloves were sold? 8

Solve each system by graphing. Check your solution. y =-3x x + y = 5 y =-7

Solve each system by graphing. Check your solution. y =-3x x + y = 5 y =-7 Practice Solving Sstems b Graphing Solve each sstem b graphing. Check our solution. 1. =- + 3 = - (1, ). = 1 - (, 1) =-3 + 5 3. = 3 + + = 1 (, 3). =-5 = - 7. = 3-5 3 - = 0 (1, 5) 5. -3 + = 5 =-7 (, 7).