Linear Systems

---

Systems of Equations

A set of equations is called a system of equations . The solutions must satisfy each equation in the system. A solution to a system is an ordered pair.

• If all equations in the system are linear, the system is called a system of linear equations, or linear system
• A system can have (1) exactly one solution, (2) no solutions, or (3) infinitely many solutions.

Four ways to solve:

1. graphing: plot ordered pairs and sketch the graphs. The point of intersection are the solutions to the system.
2. substitution: solve for one variable and substitute into the other equation.
3. multiplication
4. addition (elimination)

To solve in matlab,

a=[1 2 1; 3 2 4; 4 4 3]
b=[5;17;26]
x = inv(a)*b;
x = a/b