solve the following system of linear equation in three variables 3x‐2y+z=2 , 2x+3y- z=5 ,x+ y+z=6
Answers
Given 3 equations with 3 unknown variables, which is enough to find them.
3x-2y+z = 2. -[1]
2x+3y-z= 5. --[2]
x+y+z=6-----[3]
Step-1:
Get two equations by eliminating a variable,
(Eliminating y)
Do 2x[3]
2x+2y+2z = 12 -[4]
Do [4]+[1]
=> 5x+3z = 14 --[5]
Do 3x[3]
=> 3x+3y+3z = 18 -----[6]
Do [6]-[2]
=> x + 4z = 13 -----[7]
Y is eliminated in both [5] and [7]
Step-2: Get value of one variable using the obtained 2 equations after eliminating another variable.
(Eliminating z)
Do 5x[7]
=> 5x+20z = 65 -----[8]
Do [8]-[5]
=> 17 z = 51
=> Z = 3.
Step-3:
Use the equation to obtain another variable
Substitute in [5]
=> 5x +3(3) = 14
=> 5x = 14 - 9
=> 5x =5
=> x = 1.
Step-4:
Use another equation to obtain value of variable left.
Substitute x and z in [3]
=> 1+y+3 = 6
=> y = 6-4
=> y = 2
•°• x = 1; y = 2;z= 3