Question

6. If √ax-√by= b-a and √bx-√ay = 0, then the value of x, y ​

Answer 1

Answer:

$\mathrm{Solve\:the\:system\:of\:equations}:\quad \sqrt{a}x-\sqrt{b}y=b-a,\:\sqrt{b}x-\sqrt{a}y=0\quad :\quad \begin{pmatrix}x=-\sqrt{a},\:&y=-\sqrt{b}\end{pmatrix}$

Step-by-step explanation:

$\begin{bmatrix}\sqrt{a}x-\sqrt{b}y=b-a\\ \sqrt{b}x-\sqrt{a}y=0\end{bmatrix}$

$\mathrm{Plug\:the\:solutions\:}x=\frac{\sqrt{a}\left(b-a+\sqrt{b}y\right)}{a}\mathrm{\:into\:}\sqrt{b}x-\sqrt{a}y=0$

$\mathrm{Plug\:the\:solutions\:}y=-\sqrt{b}\mathrm{\:into\:}\sqrt{a}x-\sqrt{b}y=b-a$

$\mathrm{Therefore,\:the\:final\:solution\:for\:}\sqrt{a}x-\sqrt{b}y=b-a,\:\sqrt{b}x-\sqrt{a}y=0\mathrm{\:is\:}$

$\begin{pmatrix}x=-\sqrt{a},\:&y=-\sqrt{b}\end{pmatrix}$