2. Verificati dacă pe sisteme de ecuatii, ap a) $$ \left\{\begin{array}{l}x-\sqrt{2} y=0 \ \sqrt{2} x+y-1=0\end{array} ight. $$ b)

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2. Verificati dacă pe sisteme de ecuatii, ap a) $$ \left\{\begin{array}{l}x-\sqrt{2} y=0 \ \sqrt{2} x+y-1=0\end{array}ight. $$ b)

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Solve the system of equations $$ x-\sqrt{2}y=0;\sqrt{2}x+y-1=0 $$.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}x-\sqrt{2}	imes y=0\\sqrt{2}	imes x+y-1=0\end{array}ight.$$
- step1: Solve the equation:
  $$\left\{ \begin{array}{l}x=\sqrt{2}	imes y\\sqrt{2}	imes x+y-1=0\end{array}ight.$$
- step2: Substitute the value of $$x:$$
  $$\sqrt{2}	imes \sqrt{2}	imes y+y-1=0$$
- step3: Simplify:
  $$3y-1=0$$
- step4: Move the constant to the right side:
  $$3y=0+1$$
- step5: Remove 0:
  $$3y=1$$
- step6: Divide both sides:
  $$\frac{3y}{3}=\frac{1}{3}$$
- step7: Divide the numbers:
  $$y=\frac{1}{3}$$
- step8: Substitute the value of $$y:$$
  $$x=\sqrt{2}	imes \frac{1}{3}$$
- step9: Calculate:
  $$x=\frac{\sqrt{2}}{3}$$
- step10: Calculate:
  $$\left\{ \begin{array}{l}x=\frac{\sqrt{2}}{3}\y=\frac{1}{3}\end{array}ight.$$
- step11: Check the solution:
  $$\left\{ \begin{array}{l}x=\frac{\sqrt{2}}{3}\y=\frac{1}{3}\end{array}ight.$$
- step12: Rewrite:
  $$\left(x,yight) = \left(\frac{\sqrt{2}}{3},\frac{1}{3}ight)$$
Pe sistemele de ecuații date, soluția este $$ (x, y) = \left(\frac{\sqrt{2}}{3}, \frac{1}{3}ight) $$.
The solution to the system of equations is $$ x = \frac{\sqrt{2}}{3} $$ and $$ y = \frac{1}{3} $$.

2. Verificati dacă pe sisteme de ecuatii, ap a) \( \left\{\begin{array}{l}x-\sqrt{2} y=0 \\ \sqrt{2} x+y-1=0\end{array}\right. \) b)

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