# 3. Graphical Solution of a System of Linear Equations

A `2 ×2` **system of equations** is a set of 2
equations in 2 unknowns which must be **solved
simultaneously** (together) so that the solutions are true in
both equations.

We can solve such a system of equations **graphically**. That is, we draw the graph of the 2 lines and see where the lines intersect. The intersection point gives us the solution.

### Example 1

Solve graphically the set of equations

2

x+ 3y= 5

x− 3y= 7

## Types of solutions

A `2 ×2` system of linear equations can have three possible solutions.

### 1. Intersect at a point, so one solution only

### 2. Are parallel, so no intersection

### 3. Are identical, so intersect everywhere on the line

### Example 2

Solve graphically the system:

6

x− 3y= −12−2

x+y= 4

### Example 3

Solve graphically the system:

2

x− 3y= −6

x+y= 7

### Example 4

Solve graphically the system:

x− 5y= −10

x− 5y= 7

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