Solve the following equations by solve Gauss-Jacobi method 4x+2y+z=14, x+5y-z-10x+y+82-20
Answers
Answer:
GIVEN :
The equations are 4x+2y+z=14, x+5y-z = 10 , x+y+8z= 20
TO FIND :
The values of x, y and z
SOLUTION :
Given equations are
4x+2y+z=14 ------ (1)
x+5y-z = 10 ------- (2)
x+y+8z= 20 -------- (3)
Solving the given equations by elimination method :
Adding the equations (1) and (2) we get,
4x+2y+z=14
x+5y-z = 10
_________
5x+7y=24 ----- (4)
Multiply the equation (2) into 8
8x+40y-8z=80 ---------- (5)
Now adding the equations (5) and (3) we get
8x+40y-8z=80
x+y+8z= 20
___________
9x+41y=100 ------- (6)
Multiply the equation (4) into 9 we get
45x+63y=216 ----- (7)
Multiply the equation (6) into 5 we get
45x+205y=500 ----- (8)
Subtracting the equations (7) and (8)
45x+63y=216
45x+205y=500 (-)
_____________
-142y=-284
142y=284
y=\frac{284}{142}y=
142
284
∴ y=2
Substitute the value of y=2 in equation (6)
5x+7(2)=24
5x=24-14
5x=10
x=\frac{10}{5}x=
5
10
∴ x=2
Substitute the values of y=2 and x=2 in equation (1)
4(2)+2(2)+z=14
8+4+z=14
12+z=14
z=14-12
∴ z=2
∴ the values are x=2, y=2 and z=2