Răspuns:
Explicație pas cu pas:
[tex]I~\begin{gathered}\begin{cases}\bf x+y = 5\\\\\bf x-y = 3\end{cases}\end{gathered}\implies\begin{gathered}\begin{cases}\bf x+y = 5\\\\\bf x = 3+y\end{cases}\end{gathered}\implies\begin{gathered}\begin{cases}\bf 3+y+y = 5\\\\\bf x=3+y\end{cases}\end{gathered}[/tex]
[tex]\it~~[/tex]
[tex]\implies\begin{gathered}\begin{cases}\bf 3+2y = 5\\\\\bf x=3+y\end{cases}\end{gathered}\implies\begin{gathered}\begin{cases}\bf 2y = 2\\\\\bf x=3+y\end{cases}\end{gathered}\implies\begin{gathered}\begin{cases}\boxed{\bf y = 1}\\\\\boxed{\bf x=4}\end{cases}\end{gathered}[/tex]
[tex]\it~~~[/tex]
[tex]II~\begin{gathered}\begin{cases}\bf x+y = 1\\\\\bf 2x+3y =5\end{cases}\end{gathered}\implies\begin{gathered}\begin{cases}\bf x=1-y\\\\\bf 2(1-y)+3y=5\end{cases}\end{gathered}\implies\begin{gathered}\begin{cases}\bf x=1-y\\\\\bf 2-2y+3y=5\end{cases}\end{gathered}[/tex]
[tex]\it~~[/tex]
[tex]\implies\begin{gathered}\begin{cases}\bf x=1-y\\\\\bf y=5-2\end{cases}\end{gathered}\implies\begin{gathered}\begin{cases}\bf x=1-3\\\\\boxed{\bf y=3}\end{cases}\end{gathered}\implies\begin{gathered}\begin{cases}\boxed{\bf x=-2}\\\\\boxed{\bf y=3}\end{cases}\end{gathered}[/tex]
[tex]\it~~[/tex]
[tex]III~\begin{gathered}\begin{cases}\bf \sqrt{7} x+\sqrt{28} y = 0\\\\\bf \sqrt{63}x+\sqrt{7} y =-5\sqrt{7} \end{cases}\end{gathered}\implies \begin{gathered}\begin{cases}\bf \sqrt{7} x+2\sqrt{7} y = 0~\bigg|\cdot3\\\\\bf 3\sqrt{7}x+\sqrt{7} y =-5\sqrt{7} \end{cases}\end{gathered}\implies[/tex]
[tex]\it~~[/tex]
[tex]\begin{gathered}\begin{cases}\bf 3\sqrt{7} x+6\sqrt{7} y = 0\\\\\bf 3\sqrt{7}x+\sqrt{7} y =-5\sqrt{7} \end{cases}\end{gathered}\implies\begin{gathered}\begin{cases}\bf 3\sqrt{7} x = -6\sqrt{7}y\\\\\bf -6\sqrt{2}y+\sqrt{7} y =-5\sqrt{7} \end{cases}\end{gathered}\implies[/tex]
[tex]\it~~~[/tex]
[tex]\begin{gathered}\begin{cases}\bf 3\sqrt{7} x = -6\sqrt{7}y~\big|:_{3\sqrt{7}} \\\\\bf -5\sqrt{7}y =-5\sqrt{7} \end{cases}\end{gathered}\implies\begin{gathered}\begin{cases}\bf x = -2y\\\\\boxed{\bf y =1} \end{cases}\end{gathered}\implies\begin{gathered}\begin{cases}\boxed{\bf x = -2}\\\\\boxed{\bf y =1} \end{cases}\end{gathered}[/tex]
Bafta multa!
P.S.: Te rog sa glisezi spre stânga pentru a vedea toata rezolvarea daca esti pe telefon
==pav38==
