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Bellwork

Bellwork. Solve the following by: y = 2x y = x + 3 1.) Graphing 2.) Substitution 3.) Linear Combination (+). Show all your Work. Today’s Objective. To be able to write a linear system word problem and solve it. Example #1.

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Bellwork

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  1. Bellwork • Solve the following by: • y = 2x y = x + 3 • 1.) Graphing • 2.) Substitution • 3.) Linear Combination (+) Show all your Work

  2. Today’s Objective • To be able to write a linear system word problem and solve it.

  3. Example #1 • Read example 2 on page 368 and find the two items that were sold in the problem and the total sold. • Style A shoes • Style B shoes

  4. Example #1 • Let Style A = x • Let Style B = y • Total sold = 240 So…. • x + y = 240 (1st Equation)

  5. Example #1 • Receipts for Style A = 66.95x • Receipts for Style B = 84.95y • Total Receipts = 17,652 So…. • 66.95x + 84.95y = 17,652 (2nd Equation)

  6. Solve by Substitution • x + y = 240 • 66.95x + 84.95y = 17,652 • x + y = 240 (Solve for x) • x + y - y = 240 - y • x = 240 - y

  7. Solve by Substitution • x = 240 - y • 66.95x + 84.95y = 17,652 • 66.95(240-y) + 84.95y = 17652

  8. Solve by Substitution • 66.95(240-y) + 84.95y = 17652 • 16068 - 66.95y + 84.95y = 17652 • 16068 + 18y = 17652(subtract 16068) • 18y = 1584 (divide by 18) • y = 88 • Now Find x

  9. Solve by Substitution • Since y = 88 and • x = 240 - y then • x = 240 - 88 • x = 152 • Style A = 152, Style B = 88

  10. Steps • #1 ~ Make a list and pick the variables • #2 ~ Write the equations • #3 ~ Solve

  11. Example #2 • Read example 3 on page 369 and find the two missing items in the problem. • Total Earnings • Total Sales

  12. Example #2 • Step #1 • Let Total Sales = x • Let Total Earnings = y • Step #2 • y = 20,000 + .01x (1st job) • y = 15,000 + .02x (2nd job)

  13. Solve by (L.C. add) • y = 20,000 + .01x • y = 15,000 + .02x • y = 20,000 + .01x (times by -1) • -y = -20000 - .01x • y = 15000 + .02x (add) • You Finish to find x

  14. Solve by (L.C. add) • y = 20,000 + .01x • y = 15,000 + .02x • y = 20,000 + .01x (times by -1) • -y = -20000 - .01x • y = 15000 + .02x (add) • 0 = -5000 + .01x

  15. Solve by (L.C. add) • 0 = -5000 + .01x • 0+5000=-5000+5000+.01x • 5000 = .01x (divide by .01) • 500,000 = x • You must sell $500,000 in supplies for both jobs to be equal in salary.

  16. Solve by (L.C. add) • What salary would you earn? • Since y = 20,000 + .01x & • x = 500,000 then • y = 20,000 +.01(500000) • y = 20,000 + 5,000 • y = 25,000

  17. Classwork • Do page 370 (7,9,10) • #8 extra credit

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