Question

X+y+z=5;2x-y+z=9;x-2y+3z=16 solve system of linear equations of variable

Answer 1

Step-by-step explanation:

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Answer 2

The value of x = 2 , y=-1 and z= 4.

Explanation:

The given system of linear equations are :

$X+y+z=5$             (1)

$2x-y+z=9$             (2)

$x-2y+3z=16$            (3)

From (1) and (3) , we have

$X=5-y-z$      (4)

$x=16+2y-3z$   (5)

From (4) and (5) , we have

$5-y-z=16+2y-3z$

$\Rightarrow\ -3y+2z=11$           (6)

Put value of x from (4) in (2) , we get

$2(5-y-z)-y+z=9$  

$10-2y-2z-y+z=9$  

$-3y-z=-1$  

$z=1-3y$         (7)

Put value of z in (6) , we get

$-3y+2(1-3y)=11$

$-3y+2-6y=11$

$-9y=11-2=9$

$y=-1$

Put value of y in (7) , we get

$z=1-3(-1)=1+3=4$    

Put value of y and z in (4) , we get

$X=5-(-1)-4=5+1-4=2$

Hence, the value of x = 2 , y=-1 and z= 4.

# Learn more :

Solve, x-y+Z =4, x-2y - 2z=9, 2x+y+3z=1

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