Given X=(a+1/2b)/(a+b+c), Y=(b(sqrt3/2))/(a+b+c), Z=(76a+150b+29c)/(255) in other words How do i get a, b, and c on the left side using these three formulas?

Colten Andrade

Colten Andrade

Answered question

2022-09-23

Given
X = a + 1 2 b a + b + c
Y = b ( 3 2 ) a + b + c
Z = 76 a + 150 b + 29 c 255
in other words How do i get a, b, and c on the left side using these three formulas?

Answer & Explanation

Adelaide Barr

Adelaide Barr

Beginner2022-09-24Added 9 answers

Write in a matrix form:
( x 1 ) a + ( x 1 2 ) b + x c = 0 y a + ( y 3 2 ) b + y c = 0 76 a + 150 b + 29 c = 255 z
or
[ x 1 x 1 2 x y y 3 2 y 76 150 29 ] [ a b c ] = [ 0 0 255 z ]
so, by inversing the coefficients matrix, you will have the solution to the system of equations:
[ a b c ] = [ x 1 x 1 2 x y y 3 2 y 76 150 29 ] 1 [ 0 0 255 z ]
by doing this; you will have a , b and c in terms of x , y , z; so, you have the solutions as follows:
[ a b c ] = 255 z 29 3 + 47 3 x + 195 y [ 3 x y 2 y 3 ( 1 x ) y ]

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