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3.4 “Solving Linear Systems with 3 Variables”

3.4 “Solving Linear Systems with 3 Variables”. The solutions are called an ordered triple ( x,y,z ). Equations are in the form of Ax + By + Cz = D. 4x + 2y + 3z = 1 2x – 3 y + 5z = -14 6x – y + 4z = -1 . Steps: Number the equations 1,2,3.

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3.4 “Solving Linear Systems with 3 Variables”

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  1. 3.4 “Solving Linear Systems with 3 Variables” The solutions are called an ordered triple (x,y,z). Equations are in the form of Ax + By + Cz = D. • 4x + 2y + 3z = 1 2x – 3y + 5z = -14 6x – y + 4z = -1 Steps: • Number the equations 1,2,3. • Make an elimination plan BEFORE you start. • Put 2 equations together and eliminate a variable to get the first equation. • Put 2 DIFFERENT equations together and eliminate SAME variable to get the other equation. • Put the 2 equations together and solve by substitution or elimination. • Plug these answers in to one of the original equations to find the final variable. • Put the answer in ordered triple form.

  2. Another Example: • 2x + 3y + 2z = 14 4x + 2y – z = 15 x + y + 3z = 8 Show all work, follow steps.

  3. Try This: 3. 3x + y – 2z = 10 6x – 2y + z = -2 x + 4y + 3z = 7 Show all work, follow steps.

  4. Another Example: 4. x + y + z = 3 4x + 4y + 4z = 7 3x – y + 2z = 5 Show all work, follow steps.

  5. Tell if a Point is a Solution: 4. Is (1, 4, 3) a solution to the following problem? 2x – y + z = -5 5x + 2y – 3z = 19 x – 3y + z = -5 Plug in values for x, y, and z to see if it is true for ALL the equations.

  6. Word Problem  1. TV World had a sell on televisions. On the first day, 4 projector, 10 flat screen, and 20 hand-held televisions were sold. On the second day, 2 projectors, 30 flat screens, and 30 hand-held televisions were sold. On the third day, 3 projectors, 15 flat screen, and 25 hand-held televisions were sold. The total sales for the three days were $10,400; $16,200; and $12,300. What was the sale price for each type? Set up the equations and solve.

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