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7.3 ET: Solve

7.3 ET: Solve. Using back substitution (1, -1, 2). Use these two equations to create an equation with only x & y. Solve: Strategy 1 st create two equations w/the same two unknowns. Use these two equations to create an equation with only x & y. (1, ½, -3). Let’s get rid or y.

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7.3 ET: Solve

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  1. 7.3 ET: Solve Using back substitution (1, -1, 2)

  2. Use these two equations to create an equation with only x & y Solve: Strategy 1st create two equations w/the same two unknowns. Use these two equations to create an equation with only x & y (1, ½, -3) Let’s get rid or y.

  3. 7.3 Assignment • Day 1: 1, 5, 6, 14, 15, 21, 22, 32

  4. Solve: Using calc TI-83/84: Matrix (above x-1) rref[A] TI-89: Math (above5) rref([2,4,-1,7;2,-4,2,-6;1,4,1,0]) (1, ½, -3)

  5. Solve using calc (1, -1, 2)

  6. Solve: w/calc No Solution

  7. Solve: Use Calculator z Which variable appears in both equations? Solve for x & y in terms of z ( , , z )

  8. If you need help with story problemsLook at examples 7 & 8

  9. 7.3 Assignment • Day 1: 1, 5, 6, 14, 15, 21, 22, 32 • Day 2: 8, 12, 19, 20, 23-26, 33, 39, 43, 47 (use calculator matrix) • Day 3: 53, 57, 58, 63

  10. A mixture of 5 pounds of fertilizer A, 13 pounds of fertilizer B, and 4 pounds of fertilizer C provides the optimal nutrients for a plant. Commercial brand X contains equal parts of fertilizer B and fertilizer C. Commercial brand Y contains one part of fertilizer A and two parts of fertilizer B. Commercial brand Z contains two parts of fertilizer A, five parts of fertilizer B, and two parts of fertilizer C. How much of each fertilizer brand is needed to obtain the desired mixture?

  11. Optimal Pounds: 5A, 13B, 4C X = Lbs. bought of brand X Y = Lbs. bought of brand Y Z = Lbs. bought of brand Z Content summary of each brand. 0/2 1/3 2/9 5 x + y + z = 1/2 2/3 5/9 13 x + y + z = x + y + z = 1/2 0/3 2/9 4 X = 4 Y = 9 Z = 9

  12. The amount invested in mutual funds was $4000 more than the amount invested in municipal bonds. The total interest earned during the first year was $1120. Investment: $12,000 $7000 $2000 $3000 f = s= = t Money Market Municipal Bonds Mutual Funds 12% 5% 6% 0f – s + t = 4000 .05f + .06s + .12t = 1120 f + s + t = 12,000 t = s + 4000 .05f + .06s +.12t = 1120 f + s + t = 12,000

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