Question

Solve each system of equations.

$\begin{array}{l}2x-y+z=1\\ x+2y-4z=3\\ 4x+3y-7z=-8\end{array}$

Short answer

The solution is not possible.

Step-by-step solution

Step-1 –Using elimination to obtain two equations with two variables

Given system of equations are

$\begin{array}{l}2x-y+z=1\\ x+2y-4z=3\\ 4x+3y-7z=-8\end{array}$

Multiplying first equation by $4$and adding to the second equation, we get

localid="1648720251666" $\begin{array}{l}8x+x-4y+2y=4+3\\ 9x-2y=7\end{array}$

Again multiplying first equation by$7$and adding to the third equation, we get

$\begin{array}{l}14x+4x-7y+3y=7-8\\ 18x-4y=-1\end{array}$

Step-2 –Solving the system of two equations with two variables

System of two equations with two variables are

$\begin{array}{l}9x-2y=7\\ 18x-4y=-1\end{array}$

Step-3- Solve the second equation 

$\begin{array}{l}18x-4y=-1\\ 2(9x-4y)=-1\\ 2\left(7\right)=-1\\ 14=-1\end{array}$

Which is not possible.