Solve the following simultaneous equations: 4x + y = 14 and 6x - y = 16

First, write out the equations beneath each other:

4x + y = 14

6x - y = 16

 

Then, label the equations a and b (let's take the top one as a, and the bottom one as b)

We always look to eliminate either the x term, or the y term

Equation b + equation a would elimate the y term. i.e. -y = -1y; so, -1+1=0

Now, add the two equations together:

10x=30

Then, simplify to find out the value of a single x

x = (30/10); x = 3

 

Then, we substitute our x value into either of the equations, to work out y. 

Let's do it with equation a:

4(3) + y = 14

12 + y = 14; y= 14-12; y=2

 

We can check by putting both the x and y values into equation b to check it works:

6(3) - 2 = 16

18-2= 16

It works!!