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

2. Are parallel, so no intersection

3. Are identical, so intersect everywhere on the line

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


Search IntMath, blog and Forum

Online Algebra Solver

This algebra solver can solve a wide range of math problems.

Algebra Lessons on DVD


Easy to understand algebra lessons on DVD. See samples before you commit.

More info: Algebra videos

The IntMath Newsletter

Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!

Given name: * required

Family name:

email: * required

See the Interactive Mathematics spam guarantee.