SOLUTION: 2a-5b+c=5 3a+2b-c=17 4a+3b+2c=17

Question 55821: 2a-5b+c=5
3a+2b-c=17
4a+3b+2c=17
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
2a - 5b + c = 5
3a + 2b - c = 17
4a + 3b + 2c = 17
:
If we mult the 1st eq by -1 we can eliminate c from all three equation:
-2a + 5b - c = -5
3a + 2b - c = 17
4a + 3b + 2c = 17
---------------------add
5a + 10b = 29
:
Adding the 1st and 2nd equations eliminates c also:
2a - 5b + c = 5
3a + 2b - c = 17
-------------------add
5a - 3b = 22
:
WE have two equations with two unknowns a & b
5a + 10b = 29
5a - 3b = 22
--------------- subtract
13b = 7
b = 7/13
:
Find a using the equation 5a - 10b = 29, substitute 5/13 for b
5a + 10(7/13) = 29
5a + 70/13 = 29
5a = 377/13 - 70/13, (converted 29 to 13th)
5a = 307/13
a = (307/13) / 5
a = 307/65
:
Find c using the 1st equation, 2a - 5b + c = 5, substitute for a & b
2(307/65) - 5(7/13) + c = 5
:
614/65 - 5(35/65) + c = 5; convert 7/13 to 65th
:
614/65 - 175/65 + c = 5
:
439/65 + c = 5
:
c = 325/65 - 439/65; converted 5 to 65th
:
c = -114/65
:
So we end up with these nasty fractions (the guy who dreamed this up must be a sadist)
a = 307/65; b = 7/13; c = -114/65
:
Because of the tremendous opportunity for error here, I check these solutions using the matrix feature on the TI*83 and got the decimal equivalent for each one of these fractions.

RELATED QUESTIONS
Please show me how to solve this set of linear equations in three variables: 3a - 2b +... (answered by richwmiller)

i dont know what this is realy called but my teacher told use to do this problem & i keep (answered by edjones)

2a + 3b + c + 2d = 20 4a + b + 2c + 5d = 50 a + 2b + 3c + d = 10 2a + 4b + 2c + 3d =... (answered by Fombitz,richwmiller,sonic1)

(2a-3b)+(3a+5b) (answered by stanbon)

find the product of -3a^3b(2a^0b^4-4a^2b^3) A. -6b^5+14a^5b^4 b. 12a^5b^4-6a^3b^5 c.... (answered by Tatiana_Stebko)

Simplify a - {5b - [a - (3b - 2c) + c - (a - 2b - c)]}. (answered by DRichardson)

Find the ordered quintuplet (a,b,c,d,e) that satisfies the system of equations... (answered by math_tutor2020)

(2a-3b)(3a+2b) (answered by checkley77)

Solve 4a-3b+c=11 2a+b-4c=-1 a+2b-2c=1 By matrix inversion... (answered by Edwin McCravy)