# Thread: Forming simultaneous equations from the following?

1. ## Forming simultaneous equations from the following?

Form a pair of simultaneous equations and solve them to find x and y, given they are rational numbers.

Questions 1: x-3+√(y+2) = -1 + √5

Question 2: 1 1/2 + √(x+2y) = 3x + y + 2/3√3

Any help is appreciated
Those are 2 separate questions.

2. What you have to do is:

1) Find either x as a function of y or y as a function of x. So manipulate one of the equations till you get x=... or y=...
2) Substitute x or y in the OTHER equation and solve for the remaining variable. Now you have the value of either x or y.
3) Fill in the value for your found x or y and you'll get your second value.

Good luck!

3. Those are 2 separate questions though. I don't know how to make 2 equations out of 1.

4. Sorry my bad. Manipulate equation 1 to get $\displaystyle x+\sqrt{y+2}=2+\sqrt{5}$, now the answer lies in that $\displaystyle x,y$ are both rational.

5. Ohhh i see. Thanks (:

6. The first equation can be written as

$\displaystyle x=2+\sqrt{5}-\sqrt{y+2}.$

You're told that $\displaystyle x$ is rational, so there can't be a $\displaystyle \sqrt{5}$ on the RHS because this is irrational. It has to be removed, and the only way to do this is to put $\displaystyle y=3$, leading then to $\displaystyle x=2$.

The second equation can be solved using the same technique.