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A Linear equation in three variables x, y, and z is an equation of the form
Ax + By + Cz = D

4x + 10y + 2z = 20 To find the intercepts set two variables too zero and solve

for the third. Set y and z equal to zero and solve for x.

4x = 20

(4/4)x = 20/4

X = 5

Now set x and y or z equal to zero. It doesn’t matter which

one ill set x and z to zero.

10y = 20

(10/10)y = 20/10

Y = 2

Now set x and y equal to zero and find z. You will have

intercepts and you can now graph your triangle.

2z = 20 Z

0,0,10

(2/2)z = 20/2

Z = 10

Y

0,2,0

X

Finding the volume and surface area for rectangular solids

Formula for volume: length x height x width

Formula for surface area:

4 =

3=

=6

To get volume you multiply length x width x height

The volume would be: 4 x 3 x 6

Volume= 72 cubic units

For surface area you would find the area of each of the sides and add it together. That will get you surface area.

Because a rectangular solid has 3 pairs of congruent sides you find one of the sides and multiply it by two.

First I will find the area of side 1 (top side).

Area= 4 x 6

Area= 24

Now you multiply 24 by 2 because the opposite side has the same area.

So you get 48. That’s the area of the top and bottom sides.

Now find the area of the rest of the sides.

Area of side two= 4 x 3

Area= 12

Area of both sides= 12 x 2

Area of both sides= 24

Now find area of side 3
Area= 3 x 6

Area= 18
Area of both sides= 18 x 2

Area of both sides= 36

Now to get surface area you add up the area of all the sides.

48 + 24 + 36= 108 units²

Practice Problems

1) Find the intercepts and graph the triangle.
2x + 10y + 5z = 30

2) Find the intercepts and graph the triangle.

5x + 10y + 20z = 40

3) Find the surface area and volume of the rectangle.

	4
6

5

4) Find the surface area and volume of the rectangle.

6

12

8