The values of x,y and z in the equations are -5, 4 and 0 respectively.
How to solve simultaneous equations using elimination method.
Let's solve the system of equations by elimination.
Given
-x - 2y - z = -3 ------------------1
-2x - 3y - z = -2-----------------2
x - y + 3z = -9 ------------------3
Multiply the first equation by 2
-2x - 4y - 2z = -6
-2x - 3y - z = -2
Subtract equations 2 from the product
-y - z = -4 ---------------4
Add equations 1 &3 to eliminate x:
-x - 2y - z = -3
x - y + 3z = -9
-3y + 2z = -12 -----------------5
Let's solve equations 4 and 5 simultaneously
Multiple equation 4 by 3 and subtract the result from equation 5.
-3y -3z = -12
-3y + 2z = -12
5z = 0
z = 0
Substitute into equation 4 to find y
-y - z = -4
-y -0 = -4
-y = -4
y = 4
Substitute z = 0 and y = 4 into equation 1 to find x
-x - 2y - z = -3
-x -2(4) -0 = -3
-x - 8 = -3
-x = -3+8
= 5
x = -5
The values of x,y and z in the equations are -5, 4 and 0 respectively.