Sim equation (1 Viewer)

[MrBrightside]

solve simultaneously... x^2 + y^2 = 1 and 5 x + 12y + 13 = 0

 

[pwoh]

Dodgy method, there's probably a simpler way:

y = -5x/12 - 13/12

x^2 + (25x^2/144 + 65x/72 + 169/144) = 1
169x^2/144 + 65x/72 + 25/144 = 0
169x^2 + 130x + 25 = 0
x = -130/338 = -5/13 [using quadratic formula]
y = -12/13

 

[thongetsu]

aint it -130x/72?

 

[adomad]

aint it 130x/72?

ur not meant to have an x.....

 

[thongetsu]

but you're squaring (-5x/12 - 13/12)

 

[annabackwards]

1/ x^2 + y^2 = 1
2/ 5 x + 12y + 13 = 0

x = -(12y + 13)/5 Sub in 1/

(-(12y + 13)/5)^2 + y^2 = 1
(12y + 13)^2/25 +y^2 = 1
144y^2 - 312y + 169 + 25y^2 = 25
169y^2 -312y + 144 = 0
Solving we get y = 12/13

Sub back in x we get

x = -(12y + 13)/5 = -313/65

I think, unless i've made a mistake somewhere...

 

[MrBrightside]

nah ans is x = - 5 / 13 , y = - 12/13

 

[MrBrightside]

Dodgy method, there's probably a simpler way:

y = -5x/12 - 13/12

x^2 + (25x^2/144 + 65x/72 + 169/144) = 1
169x^2/144 + 65x/72 + 25/144 = 0
169x^2 + 130x + 25 = 0
x = -130/338 = -5/13 [using quadratic formula]
y = -12/13

where did u get the 72 from in 65x / 72?

i keep getting this... 144x^2 +155x +25 = 0 where am i going wrong?

 

[pwoh]

I just expanded y^2

y^2 = (-5x/12 - 13/12)^2
middle term simplifies to 65x/72

 

[annabackwards]

nah ans is x = - 5 / 13 , y = - 12/13

How very odd. I wonder why the difference between my answer and the actual answer is just the sign... can't spot my error either oO

 

[ascentyx]

How very odd. I wonder why the difference between my answer and the actual answer is just the sign... can't spot my error either oO

You expanded (12y + 13)^2 as 144y^2 - 312y + 169 instead of 144y^2 + 312y + 169