X-y+z=5 2y+3z=14 -3y+2z=5 solve the system useing any algebraic method?

2 Answers

Piyush Kumar Profile
Piyush Kumar answered
X-y+z=5....(1)
2y+3z=14...(2)
-3y+2z=5...(3)
multiply by 3 in eq. (2) and multiply by 2 in eq. (3) add both equation
13z = 52
z = 4
put the value of z in eq. (2)
2y+3*4=14
2y+12=14
2y=2
y = 1
put the value of y and z in eq. (1)
x-1+4=5
x+3=5
x=2

so, the point is : (2,1,4)
Oddman Profile
Oddman answered
The last two equations are suitable for elimination.
  3(2y+3z) + 2(-3y+2z) = 3(14) + 2(5)
  9z + 4z = 42+10
  13z = 52
  z = 4
Substituting into the second equation
  2y + 3(4) = 14
  y = (14 - 12)/2 = 1
Substituting into the first equation
  x - 1 + 4 = 5
  x = 5 - 3 = 2

The solution is (x, y, z) = (2, 1, 4).

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