System of equations (3 unknowns in terms of b)

[excmuffin]

Eq. 1 : (bx / 40212.4) + y ( (4/3) - (b/22619.4) ) + 2z = (50/3)

Eq. 2 : (4/3)x + y ( (32/3) - (b/22619.4) ) + 4z = (6395/24)

Eq. 3 : 2x + 8y + z = 2125/8

How do u solve this system of equations in terms of b?

Thank you

 

[Denis]

Eq. 1 : (bx / 40212.4) + y ( (4/3) - (b/22619.4) ) + 2z = (50/3)

Eq. 2 : (4/3)x + y ( (32/3) - (b/22619.4) ) + 4z = (6395/24)

Eq. 3 : 2x + 8y + z = 2125/8

How do u solve this system of equations in terms of b?

You don't need Eq.3 to solve for b.

Let u = 40212.4 and v = 22619.4

bx/u + 4y/3 - b/v + 2z = 50/3 [1]

4x/3 + 32y/3 - b/v + 4z = 6395/24 [2] ; multiply [1] by -1:
-bx/u - 4y/3 + b/v - 2z = -50/3 [1]
-------------------------------------- ; add [2] + [1]:
4x/3 - bx/u + 28y/3 + 2z = 5995/24

Finish it....

 

[Otis]

… solve this system of equations in terms of b …

… solve for b …

I don't think the OP is asking how to solve for b.

Seems like they want to solve for x,y,z in terms of b.

?

 

[HallsofIvy]

Denis, the problem was NOT to "solve for b", it was to solve for x, y, and z in terms of b. I would, slightly different from what Denis suggests, let u= 1/40212.4 and v = 1/22619.4. The equations become
bux + y ( (4/3) - bv ) + 2z = (50/3)

Eq. 2 : (4/3)x + y ( (32/3) - (bv) ) + 4z = (6395/24)

Eq. 3 : 2x + 8y + z = 2125/8

From the last equation, z= (2125/8)- 2x- 8y. Putting that into the first equation,
bux+ y(4/3+ bv)+ (2125/4)- 4x- 16y= (bu- 4)x+ (bv- 44/3)y+ 2125/4= 50/3 so (bu- 4)x+ (bv- 44/3)y= 50/3- 2125/4= 200/12- 6374/12= -6174/12= -1029/2. Putting that value of z into the second equation, (4/3)x+ ((32/3)- bv)y+ (2125/2)- 8x- 32y= -(16/3)x- (64/3- bv)y+ 2125/2= 6395/24. -(16/3)x- (64/3- bv)y= 6395/24- 12348/24= -5953/24.

So we have (bu- 4)x+ (bv- 44/3)y= -1092/2 and -(16/3)x- (64/3- bv)y= -5952/24. Solving those for x and y, in terms of b, is more tedious but should be straight forward.

 

[Denis]

"How do u solve this system of equations in terms of b?"
Did I jump to wrong conclusion?

Anyway, OP will know how to solve for b !!

 

[Steven G]

"How do u solve this system of equations in terms of b?"
Did I jump to wrong conclusion?

Anyway, OP will know how to solve for b !!

You have a system of three equations in three unknowns (x, y and z).
There are many different methods one can use. One can use elimination, substitution, cramer's rule, gaussian elimination, cheating and your favorite which is random guessing