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 $x$ ?

Question

2453 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-09T09:04:04

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

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 $x$ :

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

===================

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 $x$ .

The square of xx is equal to 4 times the square of yy. If xx is 1 more than twice yy, what is the value of xx?