Need some help on solving simultaneous equations using elimination?

Question

Solve by substitution of simultaneous equations?

x = 2y

y = x^2 - 4x + 4

Please help........

so far I have done the following...

x=2y substitute into y=x^2-4x+4

y=(2y)^2 - 4(2y) + 4

y=2y^2 - 8y + 4

Now, to take this over to the other side, I was under the impression you would do it as follows

y - 4 = 2y^2 - 8y + 4 - 4

y - 4 + 8y = 2y^2 -8y +8y

y - 4 + 8y - 2y^2 = 2y^2 - 2y^2

leaving

-2y^2 + 9y - 4 = 0

is this wrong????? can someone please help me, I asked the question earlier and got 5 totally different answers.....

Answer 1

Well, you've make a mistake

(2y)^2 is not 2y^2. It is 4y^2. You have to square the 2 as well

as the y.

so

y = 4y^2 - 8y + 4

or if you prefer

4y^2 - 8y + 4 = y  now subtract y from both sides

4y^2 - 9y + 4 = 0

and then apply quadratic equation to get y.  

Answer 2

x/2 = x² - 4x + 4

x = 2x² - 8x + 8

2x² - 9x + 8 = 0

x = [ 9 ± √ (81 - 64 ) ] / 4

x = [ 9 ± √ (17) ] / 4

Answer 3

x=2y substitute into y=x^2-4x+4

y=(2y)^2 - 4(2y) + 4

y=4y^2 - 8y + 4

4y^2 - 9y + 4 = 0