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CC Algebra Ms. Socci-pd ___ Name: ____________________ Date: ____________________ Lesson 37-Systems of Equations Algebraically Do Now: 1) Here is a system of two linear equations. Graph both in the calculator and verify that the solution to this system is (𝟑, 𝟒), by looking at the table and using the intersect key. Equation 1: 𝒚 = 𝒙 + 𝟏 Equation 2: 𝒚 = −𝟐𝒙 + 𝟏𝟎 2) Which equation represents the line that passes through the points 1 (1) y 2 x 9 (3) y x8 2 1 (2) y 2 x 3 (4) y x6 2 and There are 2 methods for solving systems algebraically. They are ___________________ and _____________________. ? Method 1: Substitution Solve this system of equations using substitution. Check. 𝑦 =𝑥+1 𝑦 = −2𝑥 + 10. 1|Page 2) Solve and check using the substitution method. y=x+5 y = 2x + 2 3) Solve and check using the substitution method. x = -y + 1 x + 3y = 9 Method 2: Elimination 2x + y = 6 x – 3y = -11 2|Page 4) Solve the following system of equations. 5) Solve the following system of equations. 𝒙− 𝒚 = 𝟏 𝟐𝒙 + 𝟑𝒚 = 𝟕 𝟑𝐱 + 𝟐𝐲 = 𝟒 𝟒𝐱 + 𝟕𝐲 = 𝟏 6) Solve the following system of equations. x + 2y = 10 x+y=6 3|Page 7) A cellular telephone company has two plans. Plan A charges $11 a month and $0.21 per minute. Plan B charges $20 a month and $0.10 per minute. After how much time, to the nearest minute, wills the cost of plan A be equal to the cost of plan B? 8) Some coins (dimes and nickels) are in a pile. The total value of the pile is $1.35. The number of nickels is one coin less than twice the number of dimes. Using a system of equations, find the number of each type of coin. 9) Bill has $2.00 in quarters and dimes. The number of quarters is 4 less than twice the number of dimes. Find the number of coins of each type. 4|Page 10) Donna wants to make trail mix made up of almonds, walnuts and raisins. She wants to mix one part almonds, two parts walnuts, and three parts raisins. Almonds cost $12 per pound, walnuts cost $9 per pound, and raisins cost $5 per pound. Donna has $15 to spend on the trail mix. Determine how many pounds of trail mix she can make. 11) The owner of a movie theater was counting the money from 1 day’s ticket sales. He knew that a total of 150 tickets were sold. Adult tickets cost $7.50 each and children’s tickets cost $4.75 each. If the total receipts for the day were $891.25, how many of each kind of ticket were sold? 12) Sharu has $2.35 in nickels and dimes. If he has a total of thirty-two coins, how many of each coin does he have? 5|Page 13) Using only 32-cent and 20-cent stamps, Charlie put $3.36 postage on a package he sent to his sister. He used twice as many 32-cent stamps as 20-cent stamps. Determine how many of each type of stamp he used. 14) A total of 600 tickets were sold for a concert. Twice as many tickets were sold in advance than were sold at the door. If the tickets sold in advance cost $25 each and the tickets sold at the door cost $32 each, how much money was collected for the concert? 15) A ribbon 56 centimeters long is cut into two pieces. One of the pieces is three times longer than the other. Find the lengths, in centimeters, of both pieces of ribbon. 6|Page 16) The ninth graders at a high school are raising money by selling T-shirts and baseball caps. The number of T-shirts sold was three times the number of caps. The profit they received for each T-shirt sold was $5.00, and the profit on each cap was $2.50. If the students made a total profit of $210, how many Tshirts and how many caps were sold? Elimination Method 1. Rewrite the equation so that x, y, =, # are lined up. 2. IF NECESSARY, Multiply both equations by the numbers that will eliminate x. AKA Flip Flop 3. Add two equations together. 4. Solve for y variable. 4. Substitute solved value into first equation to solve for x. 5. Check x and y values by substituting into second equation. 7|Page