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6-4 Application of Systems of Equations

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  1. 6-4 Application of Systems of Equations Objective: To choose best method to solve systems of equations

  2. 6-4 Application of Systems of Equations • Graphing: visual display and estimation is acceptable solution. • Substitution: when one equation is solved for one variable or is easy to solve for a variable. • Elimination: when coefficients are same or opposite or when it is not convenient to graph or substitute.

  3. 6-4 Application of Systems of Equations • Example 1: A fashion designer makes and sells hats. The material for each hat costs $5.50. The hats sell for $12.50 each. The designer spends $1400 on advertisement. How many hats must she sell to break even.

  4. 6-4 Application of Systems of Equations • Example 1: A fashion designer makes and sells hats. The material for each hat costs $5.50. The hats sell for $12.50 each. The designer spends $1400 on advertisement. How many hats must she sell to break even. • Write 2 equations and choose a method to solve. • x: number of hats sold • y: dollars of expense or income • y = 5.5x + 1400 y = 12.5x

  5. 6-4 Application of Systems of Equations • Example 2: Zoo has two water tanks that are leaking. One tank contains 10 gal of water and is leaking at a constant rate of 2 gal/hr. The other tank contains 6 gal and is leaking at a rate of 4 gal/hr. When will tanks have same amount of water?

  6. 6-4 Application of Systems of Equations • When plane travel west to east across the US, the jet stream act as a tailwind, increasing the plane’s speed. Traveling west to east, it is a headwind, slowing the speed. • West to East • Air speed + wind speed = ground speed • East to West • Air speed – wind speed = ground speed

  7. 6-4 Application of Systems of Equations • Example 3: A traveler flies from Charlotte, NC to LA, CA. At the same time, another traveler flies from LA to Charlotte. The air speed is the same for each plane. The ground speeds are 550 mi/h LA to Charlotte and 495 mi/h Charlotte to LA. What is the wind speed.

  8. 6-4 Application of Systems of Equations • You row upstream at a speed of 2mi/hr. You travel same distance down stream at 5 mi/hr. What would your rowing speed be in still water? What is the speed of current?

  9. 6-4 Application of Systems of Equations • HW p. 390 9 – 24 every third