Download Objective #1: Solve systems of equations involving three variables

Objective #1: Solve systems of equations involving three variables algebraically.
ƒ
The graph of an equation with three variables ( Ax + By + Cz = D ) is a plane in space.
The solution for a system of equations with three variables is the point(s) where the
planes intersect.
o The system has one unique solution if all three planes intersect at a point.
o The system has infinitely many solutions if all three planes interest in a line.
o The system has no solution if the three planes have no points in common.
ƒ A system of equations in three variables can be solved algebraically using
o Elimination
o Substitution
Example: Solve each linear system algebraically.
4x + 2y + z = 7
x −y −z = 7
1. 2x + 2y − 4z = −4
2. − x + 2y − 3z = −12
ƒ
x + 3y − 2z = −8
3x − 2y + 7z = 30
Modeling Example:
3. The height of an object that is thrown upward with a constant acceleration of a feet per
1
second is given by the equation s = at 2 + v 0t + s0 . The height is s feet, t represents the
2
time in seconds, v 0 is the initial velocity in feet per second, and s0 is the initial height in
feet. Find the acceleration, the initial velocity, and the initial height if the height at 1
second is 75 feet, the height at 2.5 seconds is 75 feet, and the height at 4 seconds is 3 feet.