Resolver el siguiente sistema. $$ \begin{array}{l}2 x+z=-5 \ 3 x+y=-10 \ 3 y-4 z=-6\end{array} $$ $$ y=\square $$

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Solve the system of equations $$ 2x+z=-5;3x+y=-10;3y-4z=-6 $$.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}2x+z=-5\3x+y=-10\3y-4z=-6\end{array}ight.$$
- step1: Solve the equation:
  $$\left\{ \begin{array}{l}z=-5-2x\3x+y=-10\3y-4z=-6\end{array}ight.$$
- step2: Substitute the value of $$z:$$
  $$\left\{ \begin{array}{l}3x+y=-10\3y-4\left(-5-2xight)=-6\end{array}ight.$$
- step3: Simplify:
  $$\left\{ \begin{array}{l}3x+y=-10\3y+20+8x=-6\end{array}ight.$$
- step4: Solve the equation:
  $$\left\{ \begin{array}{l}y=-10-3x\3y+20+8x=-6\end{array}ight.$$
- step5: Substitute the value of $$y:$$
  $$3\left(-10-3xight)+20+8x=-6$$
- step6: Simplify:
  $$-10-x=-6$$
- step7: Move the constant to the right side:
  $$-x=-6+10$$
- step8: Add the numbers:
  $$-x=4$$
- step9: Change the signs:
  $$x=-4$$
- step10: Substitute the value of $$x:$$
  $$y=-10-3\left(-4ight)$$
- step11: Calculate:
  $$y=2$$
- step12: Substitute the value of $$x:$$
  $$z=-5-2\left(-4ight)$$
- step13: Calculate:
  $$z=3$$
- step14: Calculate:
  $$\left\{ \begin{array}{l}x=-4\y=2\z=3\end{array}ight.$$
- step15: Check the solution:
  $$\left\{ \begin{array}{l}x=-4\y=2\z=3\end{array}ight.$$
- step16: Rewrite:
  $$\left(x,y,zight) = \left(-4,2,3ight)$$
La solución del sistema de ecuaciones es $$ x=-4, y=2, z=3 $$. Por lo tanto, $$ y=2 $$.
$$ y=2 $$

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