# Thread: simultaneous equation

1. ## simultaneous equation

hi, could someone please show me the steps involved in solving the simultaneous equation:
$\displaystyle y = x - 8$
$\displaystyle x^2 + y = 4$

and could you tell me why you choose that particular path to get the answer

thankyou, Mark

2. Originally Posted by mark
hi, could someone please show me the steps involved in solving the simultaneous equation:
$\displaystyle y = x - 8$
$\displaystyle x^2 + y = 4$

and could you tell me why you choose that particular path to get the answer

thankyou, Mark
Sub eq1 into eq2 and rearrange to get

$\displaystyle x^2+x-12=0 \: \rightarrow (x-3)(x+4)=0$

Sub those two solutions back into eq1 to give you two pairs of solutions

Spoiler:
(3,-5) and (-4,-12)

3. (1)
(2)

re arrange (2)

y = 4 - x^2

putting this back into (1)

4 - x^2 = x - 8
x^2 + x - 12 = 0
(x+4)(x-3) = 0
x = -4 or 3

when x = -4 (1) y = -4 -8 = -12 (2) (-4)^2 + y = 4 16 + y = 4 = -12

when x = 3 (1) y = 3 - 8 = -5 (2) (3)^2 + y = 4 9 + y + 4 = -5

therefore 2 answers fulfil this sim equation

x = -4 y = -12
x = 3 y = -5

I did it this way as when I saw a x squared I automatically knew it could have a negative value as well as a positive.