Mathacle PSet Algebra, Systems of Equations, Elimination Method (9.5) Level Number Name: Date:

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1 Solve each system by elimination. 1.) 2x + y = 8 3x 2y = 5 2.) 3a + 5b = 3 a + 2b = 13 3.) 3x 2y = 4 2x + y = 5 4.) 4x 3y = 7 5x y = 6 5.) 4 p q = 6 p + 2q = 13 6.) 4x 3y = 8 2x + y = 14 7.) 5 p 2q = 1 4 p + 5q = 47

2 8.) 2c 3d 3c 4d = 1 = 3 9.) 3r 2s = 15 7r 3s = ) 3c 8d = 7 c + 2d = 7 11.) 3a + b = 4 a 2b = 6 12.) x + y = 7 3x 2y = ) 4x + 5t = 22 5x t = 13 2n + 5a = ) 6n + 7a = 10

3 15.) 3p + 4q = 4 5 p + 2q = ) 3t 8z = 34 7t + 4z = ) 2c 7d = 41 6c + 5d = 7 18.) 4r + 9s = 23 7r + 3s = ) 4b + 13c = 24 12b 5c = ) 18a 5b = 17 6a + 10b = 6 3p + 8q = 8 21.) 5 p 2q = 21

4 22.) 4x + 15t = 10 3x + 10t = 5 23.) 6n + 8c 4 = 0 9n + 10c 7 = 0 24.) 6z 5t + 10 = 0 4z 7t + 25 = 0 25.) Show that the equation 6n + 4c = 5 and 9n + 6c = 8 have no common solution. 26.) Show that the equation 1 8a 10b = and a 25b = have many solutions ) 0.4x + 1.5y = x + 0.8y = x 2.1y = ) 4.6x 6.3y = 40.7

5 29.) 0.3x + 0.5y = x 0.1y = 1 30.) 0.05x y = 215 x + y = ) a b + = a b = ) x y = 9 2 y x + = ) a b 3 + = a b = 3 2 p q + = ) p 2 = q 3

6 35.) x y x y = 4 = 2 36.) Determine whether the graphs of 3x 4y = 3, 6x + 6y = 13 and 9x + 2y = 16 intersect in a single point. 37.) The point (8, 3) is the intersection of the graphs of ax + by = 25and 3ax 5by = 3. Find a and b. Solve each system by any method you prefer = 1 x y 38.) 3 2 = 8 x y

7 39.) = 5 x y 3 5 = 9 x y 40.) = 33 x y 4 35 = 43 x y Solve for x and y in terms of a and b. 41.) ax + y = 5 3ax 2y = 0 42.) ax + by = 1 3ax 2by = 4 ax by = 1 43.) bx + ay = 1

8 44.) x + y + z = 7 2x y + z = 4 3x + 2y + z = ) x + y + z = 7 2x y + z = 4 3x + 2y + z = 11 6x + 4y z = 7 46.) 5x + 6y + 2z = 14 3x 2y 3z = 13

9 Solve each of the word problems. 1.) The sum of two numbers is 25 and their difference is 7. Find the numbers. 2.) One number is 4 less than eleven times another. The sum of the two numbers is 92. Find the numbers. 3.) Cory has $24 more than twice as much as Stan. Together they have $150. How much money does each have? 4.) Marcia has $84 less than three times as much as Sue. Together they have $132. How much does each have? 5.) The length of rectangle is 5 more than twice the width. The perimeter is 130. What is the area?

10 6.) A rectangle is five times as long as it is wide. If it were 24 cm shorter and 24 cm wider, it would be a square. What are its dimensions? 7.) Phil has 50 nickels and dimes worth $4.15. How many dimes does he have? 8.) Sally has in dimes and quarters, for a total of 100 coins. How many of each kind coin does Sally have? 9.) The bill for five glasses of apple juice and four salads is $9.50, but the bill for four glasses of apple juice and five salads is $ What would be the bill for a glass of juice and a salad? 10.) Three pens and two notebooks cost $8.25. Two pens and three notebooks cost $8.00. How much would two pens and two notebooks cost? 11.) A movie theater charges $5 for an adult s ticket and $2 for a child s ticket. On Saturday the theater sold 785 tickets for $3280. How many children s tickets were sold for the movie that Saturday?

11 12.) Six grapefruit cost as much as a dozen oranges. The cost of a dozen grapefruit and two dozen oranges is $12. How many does one grapefruit cost? 13.) A chemist has 1000 g of a solution that is 40% acid. How many grams of water must be added to reduce the acidity to 25%? 14.) A chemist has 800 g of dye solution that is 20% of its original strength, how much dye must be added to increase the strength to 50%? 15.) Edna Britten s income from two stocks each year totals $280. Stock A pays dividends at rate of 5% and stock B at the rate of 6%. If she has invested a total $5,000, how much is invested in each stock? 16.) Beatrice Roberts receives $375 per year from a $6,000 investment in stocks and bonds. The bonds pay 10% interest and the stocks pay 5% in dividends. How much is invested in stocks?

12 17.) Ted s bill for 6 cans of grape juice and 4 cans of orange juice was $ When he got home, he found that he should have bought 4 cans of grape juice and 6 cans of orange juice. Although he mixed up the order, Ted did save 60 cents. How much does each can cost? 18.) Joe Tyson is the place kicker for his college football team. Last season he kicked 38 times and never missed. Each field goal scored 3 points and each point after touchdown scored 1 point for a total of 70 points. How many field goals did Joe kick last season? 19.)