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Warmups – Solve using any method. 1) y=x–6 3x – 2y = 7 2) x – y = 5 2x – 3y = 7 3) 4x + 5y = 12 4x + 3y = 4 Homework Questions? Word Problems Objective: To solve word problems involving systems of equations. WORDS THAT MEAN . . . ADD SUBTRACT MULTIPLY Sum Difference Product Plus Minus Times Increased by Decreased by Twice (x2) Subtracted Added to from Switch Order More than Less than EXAMPLE 1 1) Two numbers have a sum of 25. One number is 5 more than the other number. Find the numbers. Pick 2 variables x and y Write 2 equations x + y = 25 x=5+y Solve using . . . substitution 5 y y 25 2 y 5 25 2 y 20 y 10 Don’t forget, you get 2 answers: y = 10, x = 15 You do not have to write these as an ordered pair. EXAMPLE 2 2) The difference of two numbers is 6. Their sum is 30. Find the two numbers. Pick 2 variables x and y Write 2 equations x–y=6 x + y = 30 2 x 36 x 18 Solve using . . . elimination Don’t forget, you get 2 answers: x = 18, y = 12 EXAMPLE 3 3) The sum of two numbers is 15. One number is 4 times the other. Find the numbers. Pick 2 variables x and y Write 2 equations x + y = 15 x = 4y Solve using . . . substitution 4 y y 15 5 y 15 y3 Don’t forget, you get 2 answers: y = 3, x = 12 TOO: 1) The sum of two numbers is 32. The difference between the two numbers is 8. Find the numbers. 20, 12 1) Three times the first number plus the second number equals 20. Five times the first number minus the second number equals 12. Find the numbers. 4, 8 HOMEWORK Solving Problems with System of Equations Do both sides Tell me if you used substitution (S) or elimination (E) QUIZ next week Yippee!