SOLUTION: Solve the of equation 2x-y+z=-7, x-3y+4z=-19, and -x+4y-3z=18. A. There is one solution (-1,2,-3) B. There is one solution (1,-2,3) C. There is one solution (-1,-2,-3) D. The

Algebra ->  Radicals -> SOLUTION: Solve the of equation 2x-y+z=-7, x-3y+4z=-19, and -x+4y-3z=18. A. There is one solution (-1,2,-3) B. There is one solution (1,-2,3) C. There is one solution (-1,-2,-3) D. The      Log On


   

Question 1127836: Solve the of equation 2x-y+z=-7, x-3y+4z=-19, and -x+4y-3z=18.
A. There is one solution (-1,2,-3)
B. There is one solution (1,-2,3)
C. There is one solution (-1,-2,-3)
D. There is one solution (1,2,3)
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Solve the of equation
2x-y%2Bz=-7................eq.1
+x-3y%2B4z=-19...........eq.2
-x%2B4y-3z=18...........eq.3
-------------------------------------------------
start with
+x-3y%2B4z=-19...........eq.2
-x%2B4y-3z=18...........eq.3..........add both
-----------------------------------------------
+x-3y%2B4z-x%2B4y-3z=-19%2B18
+z%2By=-1
+z=-1-y..........(1a)

2x-y%2Bz=-7................eq.1
+x-3y%2B4z=-19...........eq.2........multiply by 2
-----------------------------------------
2x-y%2Bz=-7................eq.1.
+2x-6y%2B8z=-38...........eq.2............subtract
-----------------------------------------
2x-y%2Bz-%282x-6y%2B8z%29=-7-%28-38%29
2x-y%2Bz-2x%2B6y-8z=-7%2B38
5y-7z=31
5y-31=7z
z=%285y-31%29%2F7..........(1b)
from (1a) and (1b) we have
%285y-31%29%2F7=-1-y
5y-31=-7-7y
5y%2B7y=31-7
12y=24
highlight%28y=2%29
go to +z=-1-y..........(1a), plug in y value
+z=-1-2
+highlight%28z=-3%29
go to 2x-y%2Bz=-7................eq.1 plug in y and z value
2x-2-3=-7
2x-5=-7
2x=-7%2B5
2x=-2
highlight%28x=-1%29

answer: A. There is one solution (-1,2,-3)


Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

Solve the of equation 2x-y+z=-7, x-3y+4z=-19, and -x+4y-3z=18.
A. There is one solution (-1,2,-3)
B. There is one solution (1,-2,3)
C. There is one solution (-1,-2,-3)
D. There is one solution (1,2,3)
2x - y + z = - 7 -------- eq (i)

x - 3y + 4z = - 19 ------ eq (ii)

- x + 4y - 3z = 18 ------ eq (iii)

        y + z = - 1 -------- Adding eqs (iii) & (ii) ------ eq (iv)

- 2x + 8y - 6z = 36 -------- Multiplying eq (iii) by 2 ------ eq (v)

       7y - 5z = 29 -------- Adding eqs (v) & (i) ------ eq (vi)

       5y + 5z = - 5 ------- Multiplying eq (iv) by 5 ------ eq (vii)

12y = 24 ------ Adding eqs (vii) & (vi)

highlight_green%28matrix%281%2C5%2C+y%2C+%22=%22%2C+24%2F12%2C+%22=%22%2C+2%29%29

2 + z = - 1 ------ Substituting 2 for y in eq (iv)

highlight_green%28matrix%281%2C5%2C+z%2C+%22=%22%2C+-+1+-+2%2C+%22=%22%2C+-+3%29%29

2x - 2 + - 3 = - 7 ------ Substituting 2 for y, and - 3 for z in eq (i)

2x - 5 = - 7

2x = - 7 + 5

2x = - 2

highlight_green%28matrix%281%2C5%2C+x%2C+%22=%22%2C+%28-+2%29%2F2%2C+%22=%22%2C+-+1%29%29

Now, you choose the correct answer!