# Math Help - Algebra question

1. ## Algebra question

Hey, would appreciate any help on this, haven't had any hope with it at all

we are given the equations
x^2 = (y^2) +4
(x+0.95)^2 = ((y+1.05) ^2) +4
2.1y = 1.9x - 0.2

The question is to form a quadratic for x and then solve it and then find out terms for y.

I expanded out the second equation to y^2 - x^2 + 2.1y - 1.9x = -4.2
h/e everytime i try and replace a y value i end up with -4.2 = -4.2 or something similar.
It was based on 2 right angle triangles, first with sides 2, x, y
second with sides 2 , x + 0.95, y + 1.05

Thanks for any help in advance

2. Originally Posted by jono
Hey, would appreciate any help on this, haven't had any hope with it at all

we are given the equations
x^2 = (y^2) +4
(x+0.95)^2 = ((y+1.05) ^2) +4
2.1y = 1.9x - 0.2

The question is to form a quadratic for x and then solve it and then find out terms for y.

I expanded out the second equation to y^2 - x^2 + 2.1y - 1.9x = -4.2
h/e everytime i try and replace a y value i end up with -4.2 = -4.2 or something similar.
It was based on 2 right angle triangles, first with sides 2, x, y
second with sides 2 , x + 0.95, y + 1.05

Thanks for any help in advance
Substitute the third into the first to get:

$
20 x^2 + 19 x - 442=0
$

(Note in general three equations in two unknowns has no solution, though that does not
mean that these equations have no solution)

RonL

3. Thanks for the help

hope im not being too much bother but could anyone explain how to substitute the third into the first? im not entirely sure how

4. $2.1y = 1.9x-0.2$

So

$y \approx 0.90x - 0.095$

and $x^{2} = y^{2} + 4 = (0.90x - 0.095)^{2} + 4$ $\approx 19.0000x^{2}+17.10000x -400.902500$(slightly different from CaptainBlack depending on how you round).

From the following: $(0.90x - 0.095)^{2} + 4$ we multiply by 100 to get whole numbers (as CaptainBlack did)