Solve the system of equations usi $$ \begin{array}{c}x+y-z=2 \ 3 x+4 y-3 z=8 \ 5 x-3 y+4 z=3\end{array} $$

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Solve the system of equations $$ x+y-z=2;3x+4y-3z=8;5x-3y+4z=3 $$.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}x+y-z=2\3x+4y-3z=8\5x-3y+4z=3\end{array}ight.$$
- step1: Solve the equation:
  $$\left\{ \begin{array}{l}x=2-y+z\3x+4y-3z=8\5x-3y+4z=3\end{array}ight.$$
- step2: Substitute the value of $$x:$$
  $$\left\{ \begin{array}{l}3\left(2-y+zight)+4y-3z=8\5\left(2-y+zight)-3y+4z=3\end{array}ight.$$
- step3: Simplify:
  $$\left\{ \begin{array}{l}6+y=8\10-8y+9z=3\end{array}ight.$$
- step4: Solve the equation:
  $$\left\{ \begin{array}{l}y=2\10-8y+9z=3\end{array}ight.$$
- step5: Substitute the value of $$y:$$
  $$10-8	imes 2+9z=3$$
- step6: Simplify:
  $$-6+9z=3$$
- step7: Move the constant to the right side:
  $$9z=3+6$$
- step8: Add the numbers:
  $$9z=9$$
- step9: Divide both sides:
  $$\frac{9z}{9}=\frac{9}{9}$$
- step10: Divide the numbers:
  $$z=1$$
- step11: Substitute the values of $$y,z:$$
  $$x=2-2+1$$
- step12: Simplify:
  $$x=1$$
- step13: Calculate:
  $$\left\{ \begin{array}{l}x=1\y=2\z=1\end{array}ight.$$
- step14: Check the solution:
  $$\left\{ \begin{array}{l}x=1\y=2\z=1\end{array}ight.$$
- step15: Rewrite:
  $$\left(x,y,zight) = \left(1,2,1ight)$$
The solution to the system of equations is $$ x = 1, y = 2, z = 1 $$.
$$ x = 1, y = 2, z = 1 $$.

Solve the system of equations usi

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