Solving Systems of Equations Algebraically . Practice Examples 1 and 2 Use substitution to solve each system of equations. 1. 2x - y = 9 2. 2x - y = 7 x + 3y =-6 3. 2x + y = 5 6x - 3y = 14X - 3x - 3y = 3 * = 2 Y = 1 * = 3 Y = - 3 4. 3x + y = 7 No solution 5. 4x - y = 6 6. 2x + y = 8 4x + 2y = 16* = = 1 y = 10 2x -5 = 4X2 3 x +3 y = 12 X = y = Example 3 no solution Solve each problem. 7. BAKE SALE Cassandra and Alberto are selling pies for a fundraiser. Cassandra sold 3 small pies and 14 large pies for a total of $203. Alberto sold 11 small pies and 11 large pies for a total of $220. Determine the cost of each pie. a. Write a system of equations and solve using substitution. b. What does the solution represent in terms of this situation? c. How can you verify that the solution is correct? 8. STOCKS Ms. Patel invested a total of $825 in two stocks. At the time of her investment, one share of Stock A was valued at $12.41 and a share of Stock B was valued at $8.62. She purchased a total of 79 shares. a. Write a system of equations and solve by substitution. b. How many shares of each stock did Ms. Patel buy? How much did she invest in each of the two stocks? Examples 4-6 Use elimination to solve each system of equations. 9. 3x - 2y = 4 10. 5x + 2y = 12 11. 7x + 2y = -1 5x + 3y = -25 -6x - 2y = -14 21x + 6y =-9 12. 3x - 5y = -9 13. x - 3y =-12 14. 6w - 8z = 16 -7x + 3y = 8 2x + y = 11 3w - 42 = 8 Mixed Exercises Use substitution or elimination to solve each system of equations. 15. 0.5x + 2y = 5 16. h - z = 3 17. -r+ t = 5 x - 2y = -8 -3h + 3z =6 -2r + t = 4 18. 3r - 2t = 1 19. 5g + 4k = 10 20. 4m - 2p = 0 2r - 3t = 9 -39 -5k = 7 -3m + 9p = 5 21. The sum of two numbers is 12. The difference of the same two numbers is -4. Find the two numbers. 22. Twice a number minus a second number is -1. Twice the second number added to three times the first number is 9. Find the two numbers. Rev Solving Systems of Equations Algebraically