SIMULTANEOUS EQ URGENT 🙏🙏🙏

[frosty tundra]

yo

so how do you normally solve sim equations

like how would you solve like

2x + 3y = 6
3x + 5y = 13

[alpine hound]

so you can rearrange and equate the two

[frosty tundra]

ye

[alpine hound]

do i rearrange for i?

[frosty tundra]

or multiply one or the other

[alpine hound]

yeah

[frosty tundra]

nah you rearrange for your variables

i is a number

[alpine hound]

oh right

so

id rearrange for like w?

[frosty tundra]

yeah sure

[alpine hound]

so w=(1-(1+i)z)/1-i ?

[frosty tundra]

yep

[alpine hound]

okay so

do i expand

[frosty tundra]

well how do you normally solve sim equations again

youve got one var in terms of the other from one eqn

[alpine hound]

yep

so i sub that into the second eq

[frosty tundra]

yep!

[alpine hound]

do i then expand that

[frosty tundra]

yea

[alpine hound]

okay so

[frosty tundra]

and you probably multiply by denominator

to make it nicer

[alpine hound]

like rationalise w?

and then substitute?

[frosty tundra]

nah as in

once you sub your mess in for w

you have a fraction with 1-i on the denom

so times by 1-i

to not have a fraction

[alpine hound]

the whole thing? or just the fraction part

[frosty tundra]

well you need to multiply everything

its still an equation

having complex numbers doesnt change the main rules

[alpine hound]

ugh 😭

okay so now

ive got the whole thing in terms of i and z

[frosty tundra]

yea

remember i isnt a variable

its a number

so really you have a mess with z in it

[alpine hound]

so i can get rid of it?

[frosty tundra]

you cant get rid of it its just

you want z

and you have a bunch of other numebrs

like its no differnt from (1 - root(2))z + (1 - (1 + root(2)z)/(1 - root(2)) = 3

or whatever

[alpine hound]

what

[frosty tundra]

ive just replaced i with root(2)s

same concept

[alpine hound]

oh okay

okay so im at -4iz+2z+i -1=0

is that rigjt?

[frosty tundra]

errr im not doing the working at the same time

but from there

whats z

[alpine hound]

no wait one sec

i forgot to add the -1

okay so

i get z = 1-i/-4i+2

[frosty tundra]

so first off

you can rationalise

which you should probably do

but that is correct

[alpine hound]

okay

so

z = 4i^2 -2i-2/-20?

[frosty tundra]

simplify

[alpine hound]

z = 2i^2 -i-1/-10?

[frosty tundra]

more

[alpine hound]

z = -2i^2 +i+1/10?

[frosty tundra]

more!

[alpine hound]

wont i get a decimal in the numerator then?

[frosty tundra]

-2i^2 equals something much nicer

[alpine hound]

ohh

2

[frosty tundra]

yep

so simplify

[alpine hound]

z = +i+3/10?

[frosty tundra]

perfect

(3+i)/10

[alpine hound]

ahhh

so z = 3/10 +1/10 i

[frosty tundra]

yep

now you can use that to find w

[alpine hound]

so w=(1-(1+i)(3/10 +1/10 i)/1-i ?

[frosty tundra]

simplify that mess but yes

[alpine hound]

okay so

10-4i-2/10/1-i?

[frosty tundra]

you can definitely simplify that more

• rationalize

[alpine hound]

yep so

wait so am i dividng by 1-i or 1/1-i?

[frosty tundra]

its ((10 - 4i - 2)/10)/1-i

[alpine hound]

ahhh so

w = 3/5 +1/5i?

@frosty tundra youre a legend. thank you so much!