Simultaneous Equations Algebratically

You can do this one of two ways:

You can make the x terms equal in both the equations, I'll use your first set of equations to demonstrate this:
$[br]9x - y = 12[br]4y - 9x = 6[br]$

Multiply the second equation by -1 to get:
$[br]9x - 4y = -6[br]$

You can then proceed to subtract one from the other as follows:
$[br]9x - y = 12[br]- (9x - 4y = -6)[br]= 0x + 3y = 18[br]$

And then from there you can divide by 3 to find a value for y of 6, and then you can substitute that value back into either equation to find a value for x.



Alternatively, you can use the method of substitution, where you rearrange one equation to isolate a variable, and then substitute it into the other equation:
$[br]9x - y = 12[br]9x = 12 + y[br]y = 9x - 12[br]$

Then substitute into your other equation (4y - 9x = 6):
$[br]4(9x - 12) - 9x = 6[br]36x - 48 - 9x = 6[br]27x - 48 = 6[br]27x = 54[br]x = 2[br]$

You can then substitute this value back into either equation to find y.

Hope that helps!

I've not done maths before so I'm struggling to work it out?

I'm not sure how I'm rearranging things that's the beginning bit I'm stuck with, sounds stupid but I just don't get it.