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# Simultaneous equations

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1. How do S.E's work? i understand how to solve them i just don't understand the mechanics of it. How can we divide/add/subtract/multiply equations over each other and yield the correct answer?
2. (Original post by tryingtomaths)
How do S.E's work? i understand how to solve them i just don't understand the mechanics of it. How can we divide/add/subtract/multiply equations over each other and yield the correct answer?
Best to post examples or questions you're stuck with though I appreciate that your issue in understanding is the concept of it so..

Say we had 2x + 5 = 5y and x - 2 = y.

Now we know that there is a pair of numbers, x and y, where both of those equations are true. So you could put x - 2 = y into 2x + 5 = 5y because in both of those equations, y is the same value and x is the same value because both of the equations are true.

But instead let's multiply x - 2 = y to prove your point and show you more. Just like if we said 5 = 5, if we multiplied both sides by 2 then 'it' would still be true, but 'it' is now 10 = 10. A better example, if y = 5 then 2y = 10, but y is still = 5 and the equation is true (2*5) = 10

So x - 2 = y can become 2x - 4 = 2y, and then we can rearrange to give 2x = 2y + 4. This can directly substitute into 2x + 5 = 5y to give (2y + 4) + 5 = 5y and then solve that to give y = 3, and then we can put that into both, usually you just put one in but puting them in both shows you you've done it correctly to give x = 5.

All of that multiplying/dividing etc works because A. if you multiply all parts of an equation or divide etc by the same amount then it will be true, like 5 = 5 or y = 5 shows you. and B. when solving simultaneous equations, it's in the name - you're finding the x and y values for which the two equations have the same x and y values, which is why you can substitute.

If there are any questions please let me know

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Updated: October 13, 2016
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