# 1. Simultaneous Linear Equations

A system of simultaneous linear equations is written:

a_{1}x+b_{1}y=c_{1}

a_{2}x+b_{2}y=c_{2}

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.

### 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:

−3

x+y= 16

x− 3y= −4

One student gets the solution `x = 1`, `y = 4`, while the other student's answer is `x=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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