Solve the following system of equations x y z6 5x 2y z

Solve the following system of equations. {x - y + z=-6 5x + 2y - z = 1 -2x + 5y - z = 36 Select the correct choice below and, if necessary, fill in the answer b A. There is one solution. The solution is (Type integers or simplified fractions.) B. There are infinitely many solutions. The solution set is {(x, y, z C. The solution set is Phi.

Solution

We have x-y +z= -6…(1), 5x+2y-z= 1…(2) and -2x+5y –z = 36…(3).

On adding the 1^st and the 2^nd equations, we get x-y+z +5x+2y –z = -6+1 or, 6x+y =-5…(4). Further, on adding the 1^st and the 3^rd equations, we get x-y+z -2x +5y –z = -6+36 or, -x+4y = 30…(5). Now, on multiplying the 4^th equation by 4 and subtracting the 5^thequation from the result , we get 4(6x+y) –         (-x+4y) = -4*5 -30 or, 24x +4y+x -4y = -50 or, 25x = -50 so that x = -50/25 = -2. Now, on substituting this value of x in the 4^th equation, we get 6*-2 +y = -5 or, y = -5+12 = 7. Further, on substituting x = -2 and y = 7 in the 1^st equation, we get -2 -7 +z = -6 or, z = -6+9 = 3. Thus, there is one solution ,i.e. (x,y,z) = (-2,7,3).