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Answer:
Solving the system of equations we get:
x=2, y=4, z=-2
Step-by-step explanation:
We need to solve the system of equations
[tex]2x - y + 3z = -6\\-x + 2y - 3z = 12\\y + 5z = -6[/tex]
Let:
[tex]2x - y + 3z = -6--eq(1)\\-x + 2y - 3z = 12--eq(2)\\y + 5z = -6--eq(3)[/tex]
First we find value of y from equation 3
[tex]y+5z=-6\\y=-6-5z[/tex]
Put value of y in equation 1
[tex]2x - y + 3z = -6\\2x-(-6-5z)+3z=-6\\2x+6+5z+3z=-6\\2x+8z=-6-6\\2x+8z=-12---eq(4)[/tex]
Now, put value of y in equation 2
[tex]-x + 2y - 3z = 12\\-x+2(-6-5z)-3z=12\\-x-12-10z-3z=12\\-x-13z=12+12\\-x-13z=24--eq(5)[/tex]
Multiply equation 5 with 2 and add both equations 4 and 5
[tex]2x+8z=-12\\-2x-26z=48\\--------\\-18z=36\\z=\frac{36}{-18}\\z=-2[/tex]
So, we get z=-2
Now put value of z in equation 3
[tex]y+5z=-6\\y+5(-2)=-6\\y-10=-6\\y=-6+10\\y=4[/tex]
So, we get y=4
Now, put value of y=4, and z=-2 in equation 1
[tex]2x-y+3z=-6\\2x-4+3(-2)=-6\\2x-4-6=-6\\2x-10=-6\\2x=-6+10\\2x=4\\x=\frac{4}{2}\\x=2[/tex]
So, solving the system of equations we get:
x=2, y=4, z=-2