Algebra 2: 3.5

Three-Dimensional

1. 3-D Coordinate Plane 2. Ordered Triple (x, y, z) 3. 3 variables: x,y, z

Systems with Three Variables: Substitution

1. Choose one equation to solve for its variable (x) 2. Substitute that into each of OTHER 2 equations. 3. Write 2 new equations as system. Solve for y and z. 4. Substitute value for y and z into original equation and solve for x.

Two-Dimensional

1. Coordinate Plane 2. Ordered Pair (x,y) 3. 2 variables, x + y

Systems with Three Variables: Elimination

1. Pair together equations to eliminate x/y/z 2. Write 2 new equations as system. Solve system of 2 equations. 3. Substitute value back into ANY of original equations to solve remaining variable.

Three-Dimensional Application

Anytime you have 3 variables instead of just 2.

No Solution

No point lies in all three planes. 0 = 5 and 2 = -3

Infinite Solutions

Planes intersect along a line. 5 = 5 and 0 = 0

One Solution

Planes intersect at one single point.

Graphing Equations in Three Dimensions

To sketch plane, find three points x, y, z intercepts.

Coordinates of Graphing Equations

X-int: (x, 0, 0) Y-int: (0, y, 0) Z-in: (0, 0, z)