จงหาคำตอบของระบบสมการ $$ 2 x+y=2 $$ $$ x+3 y=1 $$

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Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}2x+y=2\x+3y=1\end{array}ight.$$
- step1: Solve the equation:
  $$\left\{ \begin{array}{l}y=2-2x\x+3y=1\end{array}ight.$$
- step2: Substitute the value of $$y:$$
  $$x+3\left(2-2xight)=1$$
- step3: Simplify:
  $$-5x+6=1$$
- step4: Move the constant to the right side:
  $$-5x=1-6$$
- step5: Subtract the numbers:
  $$-5x=-5$$
- step6: Change the signs:
  $$5x=5$$
- step7: Divide both sides:
  $$\frac{5x}{5}=\frac{5}{5}$$
- step8: Divide the numbers:
  $$x=1$$
- step9: Substitute the value of $$x:$$
  $$y=2-2	imes 1$$
- step10: Substitute back:
  $$y=2-2$$
- step11: Calculate:
  $$y=0$$
- step12: Calculate:
  $$\left\{ \begin{array}{l}x=1\y=0\end{array}ight.$$
- step13: Check the solution:
  $$\left\{ \begin{array}{l}x=1\y=0\end{array}ight.$$
- step14: Rewrite:
  $$\left(x,yight) = \left(1,0ight)$$
คำตอบของระบบสมการคือ $$ (x, y) = (1, 0) $$ ซึ่งหมายความว่า $$ x = 1 $$ และ $$ y = 0 $$
$$ x = 1 $$ และ $$ y = 0 $$

จงหาคำตอบของระบบสมการ \( 2 x+y=2 \) \( x+3 y=1 \)

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