Question

Use substitution to solve the following system of linear equations and fill in the following blanks:

x + y + z = -6
x - 6y - 7z = -29
-7y - 5z = 4
In the first step, select Equation 1 and find an expression for variable X in terms of other variables:
x = - y -z - 6
Then substitute X in Equation 2. The result is the following new equation:
___y+___ z = -23
In the last step, using back-substitution, the solution for this system is:
x=
y=
Z=

Answer 1

`x=-4`

`y=3`

`z=-5`

Explanation:

Given:

`x+y+z=-6`

`x-6y-7z=-29`

`-7y-5z=4`

Solve for
`x` in the 1st equation:

`x+y+z=-6`

`x+y=-z-6`

`x=-y-z-6`

Substitute the value of
`x` into the 2nd equation and solve for
`z`:

`x-6y-7z=-29`

`(-y-z-6)-6y-7=-29`

`-7y-z-13=-29`

`-7y-z=-16`

`-z=-16+7y`

`z=16-7y`

Substitute the value of
`z` into the 3rd equation and solve for
`y`:

`-7y-5z=4`

`-7y-5(16-7y)=4`

`-7y-80+35y=4`

`28y-80=4`

`28y=84`

`y=3`

Plug
`y=3` into the solved expression for
`z` and evaluate to solve for
`z`:

`z=16-7(3)`

`z=16-21`

`z=-5`

Plug
`z=-5` into the solved expression for
`x` and evaluate to solve for
`x`:

`x=-(3)-(-5)-6`

`x=-3+5-6`

`x=2-6`

`x=-4`

Therefore:

`x=-4`

`y=3`

`z=-5`