1. Solving Systems of Three
Linear Equations in Three
Variables
The Elimination Method
LEQ How to solve systems of three linear equations in three variables?
2. Solutions of a system with 3 equations
The solution to a system of three
linear equations in three
variables is an ordered triple.
(x, y, z)
The solution must be a solution
of all 3 equations.
3. Is (–3, 2, 4) a solution of this system?
3x + 2y + 4z =
11
2x – y + 3z = 4
5x – 3y + 5z =
–1
3(–3) + 2(2) + 4(4) =
11
2(–3) – 2 + 3(4) = 4
5(–3) – 3(2) + 5(4) =
–1
Yes, it is a solution to the system
because it is a solution to all 3
equations.
4. Methods Used to Solve Systems in 3 Variables
1. Substitution
2. Elimination
3. Cramer’s Rule
4. Gauss-Jordan Method
….. And others
5. Why not graphing?
While graphing may technically be
used as a means to solve a system
of three linear equations in three
variables, it is very tedious and
very difficult to find an accurate
solution.
The graph of a linear equation in
three variables is a plane.
6. This lesson will focus on the
Elimination Method.
7. Use elimination to solve the following
system of equations.
x – 3y + 6z = 21
3x + 2y – 5z = –30
2x – 5y + 2z = –6
8. Step 1
Rewrite the system as two smaller
systems, each containing two of the
three equations.
10. Step 2
Eliminate THE SAME variable in each
of the two smaller systems.
Any variable will work, but sometimes
one may be a bit easier to eliminate.
I choose x for this system.
Be the first to comment