1. Simultaneous Linear Equations

A system of simultaneous linear equations is written:

a1x + b1y = c1
a2x + b2y = c2

Our aim in this chapter is to find values (x, y) which satisfy both equations.

First, we will test a solution to see what it means. In later sections, we will see how to find the solution.

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Example

Two students are working on a chemistry problem involving 2 variables, x and y. They obtain this system of 2 equations in 2 unknowns:

−3x + y = 1

6x − 3y = −4

One student gets the solution x = 1, y = 4, while the other student's answer is x = \large{\tfrac{1}{3}}, y = 2.

Who is correct?

We revise straight lines before seeing how to solve this kind of simultaneous equation using a graph.

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