# Thread: Non-Linear Simultaneous equations

1. ## Non-Linear Simultaneous equations

hi all im clueless about some of these problems, i hope there are only a few of these clueless ones to memorise

y = 1/x
y= 2x - 1

and

y= 2 times square root X minus 3
y = X -6

and also

y = 4 sin x
y = 2x + 1

please solve with explanations, thanks!

2. First one:

y= 2x - 1
Try rearranging this equation to get x by itself.

You should get x = (y + 1) / 2

Now, from here, plug this value of x into your other equation. This should get rid of any x's in your equation, making it possible to solve.

y = 1/x

Turns into

y = 1/[(y + 1)/2]

You're dividing by another fraction so multply it by it's reciprocal.

y = (1 * 2) / [(y + 1) * 1]
y = 2/(y + 1)
y(y+1) = 2
y² + y - 2 = 0
(y - 1)(y + 2)

The answer is 1 and -2.

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From here, you should be able to do the other two. Just remember to always get x by itself.