Question

Solve using elimination -x+6y-3z=-12 / -4x-y-4z=7 /-x+y+5z=-6

Answer 1

Given the equations

`\begin{gathered} -x+6y-3z=-12 \\ -4x-y-4z=7 \\ -x+y+5z=-6 \end{gathered}`

Since the first and third equations have the same leading coefficients, the first step will be to subtract them to eliminate the variable x:

The result is 5y-8z=-6

The second, step is to select another pair of equations and subtract them to eliminate the variable x.

For example the first and second equations.

To be able to eliminate the variable x, first, you have to multiply the first equation by 4 so that it has the same leading coefficient as the second equation:

-Multiply the first equation by 4:

`\begin{gathered} 4\cdot(-x+6y-3z)=4\cdot(-12) \\ 4\cdot(-x)+4\cdot6y-4\cdot3z=-48 \\ -4x+24y-12z=-48 \end{gathered}`

-Subtract the result obtained and the second equation:

The result is 25y-8z=-55

Now you have to work with the equations 5y-8z=-6 and 25y-8z=-55, to find the values of z and y:

-Express 5y-8z=-6 in terms of y

`\begin{gathered} 5y-8z=-6 \\ 5y-8z+8z=-6+8z \\ 5y=8z-6 \\ (5y)/(5)=(8z)/(5)-(6)/(5) \\ y=(8)/(5)z-(6)/(5) \end{gathered}`

-Replace this expression into 25y-8z=-55, and calculate for z: