Easy Mathematical Equation?

Question

If a=5b
b=2c-3
c=-3d
d=-2a
e=? when -2b+3c=2a+2b-e

Answer 1

the trick is to change all those weird as* unknowns into one weird as* unknown.

since b = 2c - 3,

- 2b + 3c = 2a + 2b - e would be:
-2 (2c - 3) + 3c = 2a + 2 (2c - 3) - e

a = 5b and b = 2c - 3
so a = 5(2c - 3) = 10c - 15

so -2 (2c - 3) + 3c = 2a + 2 (2c - 3) - e can now be:
-2 (2c - 3) + 3c = 2 (10c - 15) + 2 (2c - 3) - e
-4c + 6 + 3c = 20c - 30 + 4c - 6 - e
-25c = - 42 - e
25c = 42 + e
e = 25c - 42 ------------------- equation 1.

e = 25 (-3d) - 42 = -75d - 42 = 150a - 42 = 750b - 42
= 750(2c - 3) - 42
= 1500c - 2250 - 42
= 1500c - 2292 ------------- equation 2.

equation 1 = equation 2

25c - 42 = 1500c - 2292
2250 = 1475c
c = 90/59

substitute this back into equation 1:
e = 25 (90/59) - 42
= -228/59 = -3.86

this is what math guy got too... lol. pretty confusing question at first! haha thanks!

Answer 2

express the first 4 equations in the form [A+B+C+D= Constant] like this:

1A - 5B + 0C + 0D = 0
0A + 1B - 2C + 0D = -3
0A + 0B + 1C + 3D = 0
2A + 0B + 0C + 1D = 0

this is a system of 4 equations in 4 variables. Solve this system to get A,B,C,D,E.

OR DO THIS:

D = -2(5B) since A=5B
D=-10B
so C = -3(-10B)
C = 30B

plugging in: B = 2(30B) - 3
B = 60B - 3
hence: B = 3/59

backsubbing: A = 5(3/59) = 15/59
D = -2(15/59) = -30/59
C = -3(-30/59) = 90/59

therefore: E = 2A+4B-3C = 2(15/59)+4(3/59)-3(90/59)
= 30/59 + 12/59 - 270/59
= -228/59

Answer 3

-3.8644067796610169491525423728814

the calculation is :

d= -2a = -2 ( 5b) = -10b

c= -3d = -3 ( -10b ) = +30b = 30b

b= 2c-3 = 2 ( 30b ) -3 = 60b -3

i.e.:
b= 60b-3
3= 60b - b
3 = 59b
b= 3/59

a=5b= 15/59

d= -2a= -30/59

c= -3d= -3 (-30/59) = 90/59

-2b + 3c = 2a + 2b - e
e= 2a+2b+2b-3c
e= 2 (15/59) + 2 (3/59) + 2 (3/59) - 3 (90/59)
e= 42/59 - 270/59
e= -3.8644067796610169491525423728814

Hey...thanks for brain storming after leaving collage. :)

Answer 4

The answer is endless like below
-2b + 3c = 2a + 2b - e
-2(2c-3)+3c = 2(5b)+2b-e
-4c+6+3c = 10b+2b-e
-c+6 = 12b-e
e = 12b+c-6
= 12(2c-3)+c-6
= 24c-36+c-6
=25c-42
Plug in c=3d and plug in d=2a and............................

Answer 5

If a=5b, then d=-10b, d=-20c+30, d=60d+30, which means that 59d=-30, or d=-30/59. From this it follows that c=90/59, b=3/59, a=15/59. Rearranging the last equation gives e=2a+4b-3c, which by substitution gives e=30/59+12/59-270/59=-228/59.

So e=-228/59. Q.E.D.

Answer 6

-2b+3c=2a+2b-e
-2*[2c-3]+3[-3d] = 2[5b]+2[2c-3]-e
-4c+6-9d = 10b+4c-6-e
-4c-4c+6+6-9d-10b = -e
-8c+12-9d-10b = -e
8c-12+9d+10b = e
2[c+5b]+3[3d-4] = e

Answer 7

-2b + 3c = 2a+2b-e

-2b + 2b cancels each other out

3c =2A -e

E= 2A-3C
or e = 10b + 9d

thats my guess

Answer 8

Are u serious that isn't easy ... I haen't done that type of work in a long time. I came up with e=10b+8C+9d-9

Answer 9

-75(2a)-42=e
this can also more valued
remaining is for your brain

Answer 10

e=10b+8c+9d-12