Question

Solve the system of equations,

$\left\{\begin{array}{l}4x-3y+2z=0\\ -2x+3y-7z=1\\ 2x-2y+3z=6\end{array}\right.$

Short answer

The system of equations has no solution.

Step-by-step solution

Step 1. Given the information.

The system of equations is,

$\left\{\begin{array}{l}4x-3y+2z=0............\left(1\right)\\ -2x+3y-7z=1.........\left(2\right)\\ 2x-2y+3z=6............\left(3\right)\end{array}\right.$

Step 2. Eliminating x from equations (1) and (2).

Eliminating $x$from equations (1) and (2).

$$\begin{gathered} 4x-3y+2z=0.........\left(1\right) \\ -4x+6y-14z=2....\left(2\right)\times 2 \end{gathered}$$

Solving the equations we get,

role="math" localid="1644563835774" $3y-12z=2........\left(4\right)$

Step 3. Eliminating x from the equations (2) and (3).

Eliminating $x$from equations (2) and (3).

$$\begin{gathered} -2x+3y-7z=1......\left(2\right) \\ 2x-2y+3z=6........\left(3\right) \end{gathered}$$

Solving the equations we get,

$y-4z=7........\left(5\right)$

Step 4. Finding the value of z.

Solving equations (4) and (5),

$$\begin{gathered} 3y-12z=2...........\left(4\right) \\ 3y-12z=21............\left(5\right)\times 3 \end{gathered}$$

Subtracting the equations we get,

$0=-19$

The system of equations has no solution.