Question

5x-4y-6z = -3
X-3y+z=-1
-3x-6y+7z=1

Answer 1

To solve the given system of equations, we can use the method of elimination. The solution is x = 2, y = -1, and z = 1.

Step-by-step explanation:

To solve the given system of equations:

5x-4y-6z = -3
X-3y+z=-1
-3x-6y+7z=1

We can use the method of substitution or elimination to solve for the values of x, y, and z.

Let's use the method of elimination:

1. Multiply the second equation by 5 and the third equation by 3 in order to make the coefficients of x in the second and third equations equal to that of the first equation.
2. Add the resulting equations together to eliminate x:
3. Solve the resulting system to find the values of y and z.
4. Substitute the values of y and z back into any of the original equations to solve for x.

The solution is x = 2, y = -1, and z = 1.

Answer 2

`x=-(41)/(55),y=(2)/(55),z=-(8)/(55)`

Step-by-step explanation:

`5x-4y-6z=-3...............eq(1)\\\\x-3y+z=-1.....................eq(2)\\\\-3x-6y+7z=1.................eq(3)`

`eq(1)-5* eq(2)`

`5x-4y-6z-5(x-3y+z)=-3-5* (-1)\\\\11y-11z=2\\\\y-z=(2)/(11)...................eq(4)`

`3* eq(2)+eq(3)`

`3(x-3y+z)-3x-6y+7z=3* (-1)+1\\\\-15y+10z=-2\\\\-y+(2)/(3)z=-(2)/(15).........eq(5)`

`eq(4)+eq(5)`

`y-z-y+(2)/(3)z=(2)/(11)-(2)/(15)\\\\-(1)/(3)z=(8)/(165)\\\\z=-(8* 3)/(165)\\\\z=-(8)/(55)`

From
`eq(4)`

`y=z+(2)/(11)=-(8)/(55)+(2)/(11)\\\\y=(2)/(55)`

Substitute the value of
`y` and
`z` in
`eq(2)`

`x-3* (2)/(55)-(8)/(55)=-1\\\\x-(14)/(55)=-1\\\\x=-1+(14)/(55)\\\\x=(41)/(55)`