Question

2x - y + 3z = -6
-x + 2y - 3z = 12
y + 5z = -6

Answer 1

Solving the system of equations we get:

x=2, y=4, z=-2

Explanation:

We need to solve the system of equations

`2x - y + 3z = -6\\-x + 2y - 3z = 12\\y + 5z = -6`

Let:

`2x - y + 3z = -6--eq(1)\\-x + 2y - 3z = 12--eq(2)\\y + 5z = -6--eq(3)`

First we find value of y from equation 3

`y+5z=-6\\y=-6-5z`

Put value of y in equation 1

`2x - y + 3z = -6\\2x-(-6-5z)+3z=-6\\2x+6+5z+3z=-6\\2x+8z=-6-6\\2x+8z=-12---eq(4)`

Now, put value of y in equation 2

`-x + 2y - 3z = 12\\-x+2(-6-5z)-3z=12\\-x-12-10z-3z=12\\-x-13z=12+12\\-x-13z=24--eq(5)`

Multiply equation 5 with 2 and add both equations 4 and 5

`2x+8z=-12\\-2x-26z=48\\--------\\-18z=36\\z=(36)/(-18)\\z=-2`

So, we get z=-2

Now put value of z in equation 3

`y+5z=-6\\y+5(-2)=-6\\y-10=-6\\y=-6+10\\y=4`

So, we get y=4

Now, put value of y=4, and z=-2 in equation 1

`2x-y+3z=-6\\2x-4+3(-2)=-6\\2x-4-6=-6\\2x-10=-6\\2x=-6+10\\2x=4\\x=(4)/(2)\\x=2`

So, solving the system of equations we get:

x=2, y=4, z=-2