# 4. Algebraic Solutions of Linear Systems

## a. Solving Systems of Equations Using Substitution

This method involves subsituting *y* (or `x` if it is easier) from one equation into the other equation. This simplifies the second equation and we can solve it easily.

### Example 1

Solve the system

x+y= 3 [1]3

x− 2y= 14 [2]

using substitution.

(The numbers in square brackets, [1] and [2], are used to name each equation. This makes it easier when referring to them in the solution.)

## b. Solving Systems of Equations Using Elimination

Our aim here is to **eliminate** one of the variables. It doesn't matter which one - we usually just do the easiest one.

**Example 2 **

Solve the system using elimination.

3

x+y= 10 [1]

x− 2y= 1 [2]

In a later chapter we will see how to solve systems of equations using **determinants** (okay for paper-based solutions) and **matrices** (very powerful and the best way to do it on computers).

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