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

2x + 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

Graph of the linear equations y = x+3 and y = -2x+13.

2. Are parallel, so no intersection

Graph of the linear equations y = -x+3 and y = -x+7.

3. Are identical, so intersect everywhere on the line

Graph of the linear equations x+y = 6 and 2x+2y = 12.

Continues below

Example 2

Solve graphically the system:

6x − 3y = −12

−2x + y = 4

Example 3

Solve graphically the system:

2x − 3y = −6

x + y = 7

Example 4

Solve graphically the system:

x − 5y = −10

x − 5y = 7