The solution to the system below is $$ (1,-3) $$. $$ 2 y+x=-5 $$ and $$ y-3 x=-6 $$

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Solve the system of equations $$ 2y+x=-5;y-3x=-6 $$.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}2y+x=-5\y-3x=-6\end{array}ight.$$
- step1: Solve the equation:
  $$\left\{ \begin{array}{l}x=-5-2y\y-3x=-6\end{array}ight.$$
- step2: Substitute the value of $$x:$$
  $$y-3\left(-5-2yight)=-6$$
- step3: Simplify:
  $$7y+15=-6$$
- step4: Move the constant to the right side:
  $$7y=-6-15$$
- step5: Subtract the numbers:
  $$7y=-21$$
- step6: Divide both sides:
  $$\frac{7y}{7}=\frac{-21}{7}$$
- step7: Divide the numbers:
  $$y=-3$$
- step8: Substitute the value of $$y:$$
  $$x=-5-2\left(-3ight)$$
- step9: Simplify:
  $$x=1$$
- step10: Calculate:
  $$\left\{ \begin{array}{l}x=1\y=-3\end{array}ight.$$
- step11: Check the solution:
  $$\left\{ \begin{array}{l}x=1\y=-3\end{array}ight.$$
- step12: Rewrite:
  $$\left(x,yight) = \left(1,-3ight)$$
The solution to the system of equations is $$ (1,-3) $$, which means that the values of $$ x $$ and $$ y $$ that satisfy both equations are $$ x = 1 $$ and $$ y = -3 $$.
The solution is $$ x = 1 $$ and $$ y = -3 $$.

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