Question

The square of `x` is equal to 4 times the square of `y`. If `x` is 1 more than twice `y`, what is the value of `x`?

Answer 1

`x = 1/2`, `y = -1/4`

Explanation:

Let's describe the situation in equations.

The first sentence can be written as

`x^2 = 4y^2`

and the second one as

`x = 1 + 2y`

So now we have two equations that we can solve for `x` and `y`.

To do so, let's plug the second equation into the first equation, so plug `1 + 2y` for every occurence of `x` in the first equation:

`(1 + 2y)^2 = 4y^2`

`1 + 4y + 4y^2 = 4y^2`

... subtract `4y^2` on both sides...

`1 + 4y = 0`

... subtract `1` on both sides...

`4y = -1`

...divide by `4` on both sides...

`y= - 1/4`

Now that we have `y`, we can plug the value into the second equation to find `x`:

`x = 1 + 2* (-1/4) = 1 - 1/2 = 1/2`

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You can make a quick check if `x` and `y` were computed correctly:

• the square of `x` is `(1/2)^2 = 1/4`, the square of `y` is `(-1/4)^2 = 1/16`. The square of `x` is indeed equal to `4` times the square of `y`.
• twice `y` is `-1/2`, and one more is `-1/2 + 1 = 1/2` which is indeed `x`.