2.a Résoudre le système suivant: $$ \left\{\begin{array}{l}2(x+y)^{2}+5(x-y)^{2}=143 \ 3(x+y)^{2}-4(x-y)^{2}=-73\end{array} ight. $$

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2.a Résoudre le système suivant: $$ \left\{\begin{array}{l}2(x+y)^{2}+5(x-y)^{2}=143 \ 3(x+y)^{2}-4(x-y)^{2}=-73\end{array}ight. $$

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Solve the system of equations $$ 2(x+y)^{2}+5(x-y)^{2}=143;3(x+y)^{2}-4(x-y)^{2}=-73 $$.
Solve the system of equations by following steps:
- step0: Solution:
  $$\left\{ \begin{array}{l}2\left(x+yight)^{2}+5\left(x-yight)^{2}=143\3\left(x+yight)^{2}-4\left(x-yight)^{2}=-73\end{array}ight.$$
- step1: Solve using substitution:
  $$\left\{ \begin{array}{l}2t+5v=143\3t-4v=-73\end{array}ight.$$
- step2: Solve the equation:
  $$\left\{ \begin{array}{l}t=\frac{143-5v}{2}\3t-4v=-73\end{array}ight.$$
- step3: Substitute the value of $$t:$$
  $$3	imes \frac{143-5v}{2}-4v=-73$$
- step4: Simplify:
  $$\frac{3\left(143-5vight)}{2}-4v=-73$$
- step5: Multiply both sides of the equation by LCD:
  $$\left(\frac{3\left(143-5vight)}{2}-4vight)	imes 2=-73	imes 2$$
- step6: Simplify the equation:
  $$429-23v=-146$$
- step7: Move the constant to the right side:
  $$-23v=-146-429$$
- step8: Subtract the numbers:
  $$-23v=-575$$
- step9: Change the signs:
  $$23v=575$$
- step10: Divide both sides:
  $$\frac{23v}{23}=\frac{575}{23}$$
- step11: Divide the numbers:
  $$v=25$$
- step12: Substitute the value of $$v:$$
  $$t=\frac{143-5	imes 25}{2}$$
- step13: Simplify:
  $$t=9$$
- step14: Calculate:
  $$\left\{ \begin{array}{l}t=9\v=25\end{array}ight.$$
- step15: Evaluate:
  $$\left\{ \begin{array}{l}\left(x+yight)^{2}=9\\left(x-yight)^{2}=25\end{array}ight.$$
- step16: Solve the equation:
  $$\left\{ \begin{array}{l}x=3-y\cup x=-3-y\\left(x-yight)^{2}=25\end{array}ight.$$
- step17: Evaluate:
  $$\left\{ \begin{array}{l}x=3-y\\left(x-yight)^{2}=25\end{array}ight.\cup \left\{ \begin{array}{l}x=-3-y\\left(x-yight)^{2}=25\end{array}ight.$$
- step18: Calculate:
  $$\left\{ \begin{array}{l}x=-1\y=4\end{array}ight.\cup \left\{ \begin{array}{l}x=4\y=-1\end{array}ight.\cup \left\{ \begin{array}{l}x=-4\y=1\end{array}ight.\cup \left\{ \begin{array}{l}x=1\y=-4\end{array}ight.$$
- step19: Rearrange the terms:
  $$\left\{ \begin{array}{l}x=-1\y=4\end{array}ight.\cup \left\{ \begin{array}{l}x=-4\y=1\end{array}ight.\cup \left\{ \begin{array}{l}x=1\y=-4\end{array}ight.\cup \left\{ \begin{array}{l}x=4\y=-1\end{array}ight.$$
- step20: Check the solution:
  $$\left\{ \begin{array}{l}x=-1\y=4\end{array}ight.\cup \left\{ \begin{array}{l}x=-4\y=1\end{array}ight.\cup \left\{ \begin{array}{l}x=1\y=-4\end{array}ight.\cup \left\{ \begin{array}{l}x=4\y=-1\end{array}ight.$$
- step21: Rewrite:
  $$\left(x,yight) = \left(-1,4ight)\cup \left(x,yight) = \left(-4,1ight)\cup \left(x,yight) = \left(1,-4ight)\cup \left(x,yight) = \left(4,-1ight)$$
Le système d'équations donné a quatre solutions possibles: 
1. $$ (x,y) = (-1,4) $$
2. $$ (x,y) = (-4,1) $$
3. $$ (x,y) = (1,-4) $$
4. $$ (x,y) = (4,-1) $$
Le système d'équations a quatre solutions possibles: 1. $$ (x,y) = (-1,4) $$ 2. $$ (x,y) = (-4,1) $$ 3. $$ (x,y) = (1,-4) $$ 4. $$ (x,y) = (4,-1) $$

2.a Résoudre le système suivant:

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