3 5 Linear Equations in Three Variables

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3. 5 Linear Equations in Three Variables

Do Now §Grab some slides from the front. §Take out your homework and check your answers. The answers are found in the slides. (Note: Answers to the classwork from yesterday are posted online. )

#4 x: number of ounces of Food X y: number of ounces of Food Y C=0. 2 x+0. 3 y Corner Points: (0, 4) (0, 5) (3, 0) (5, 0) (1, 2) Minimum of $0. 60 for (3, 0), so use 3 oz. of Food X.

That’s a Matador!

Coordinate Graph in Three Variables

8 Octants I. x > 0, y > 0, z > 0 V. x > 0, y > 0, z < 0 II. x > 0, y < 0, z > 0 VI. x > 0, y < 0, z < 0 III. x < 0, y < 0, z > 0 VII. x < 0, y < 0, z < 0 IV. x < 0, y > 0, z > 0 VIII. x < 0, y > 0, z < 0

Plot (-2, 3, 2)

Graph 3 x+2 y+4 z=12

Graph 6 x-3 y+9 z=36

Write the Equation of the Plane Given the Intercepts • • ax+by+cz=d form Example: x-intercept 1/2, y-intercept 1, z-intercept -5/2 Points (1/2, 0, 0), (0, 1, 0), (0, 0, -5/2) Now • Divide by d:

Need first coefficient positive and all coefficients as integers, so multiply by 5. Answer:

You Try! Find the equation of the plane with x-intercept of 4, y-intercept of -2, and z-intercept of 4 in standard form. x-2 y+z=4

f(x, y) Write 3 x-12 y+5 z=30 as a function of x and y in function notation. Find f(-2, 2). Isolate “z”. Replace “z” with f(x, y).

Application You are buying tulips, carnations, and a glass vase to make a flower arrangement. The flower shop sells tulips for $. 70 each and carnations for $. 30 each. The glass vase costs $12. Write a model for the total cost of the flower arrangement as a function of the number of tulips and carnations you use. How much would it cost for 10 tulips and 5 carnations? t=number of tulips, c=number of carnations f(t, c)=. 70 t+. 30 c+12 f(10, 5)=. 70(10)+. 30(5)+12=$20. 50

For You! You want to buy an aquarium and stock it with goldfish and angelfish. The pet store sells goldfish for $. 40 each and angelfish for $4 each. The aquarium starter kit costs $65. Write a model for the amount you will spend as a function of the number of goldfish and angelfish you buy. How much do you pay if you buy 6 goldfish and 10 angelfish?

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