a) Ta có:
\(D = \left| \matrix{ 5\,\,\,\, - 4 \hfill \cr 7\,\,\,\, - 9 \hfill \cr} \right| = - 45 + 28 = - 17\)
\({D_x} = \left| \matrix{ 3\,\,\,\,\,\, - 4 \hfill \cr 8\,\,\,\,\,\, - 9 \hfill \cr} \right| = - 27 + 32 = 5\)
\({D_y} = \left| \matrix{ 5\,\,\,\,\,\,\,3 \hfill \cr 7\,\,\,\,\,\,8 \hfill \cr} \right| = 40 - 21 = 19\)
Hệ có nghiệm:
\(\left\{ \matrix{ x = {{{D_x}} \over D} = {{ - 5} \over {17}} \hfill \cr y = {{{D_y}} \over D} = - {{19} \over {17}} \hfill \cr} \right.\)
b) Ta có:
\(D = \left| \matrix{ \sqrt 3 \,\,\,\,\,\,\,\sqrt 2 \hfill \cr 2\sqrt 2 \,\,\,\,\sqrt 3 \hfill \cr} \right| = 3 - 4 = - 1\)
\({D_x} = \left| \matrix{ - 1\,\,\,\,\,\,\sqrt 2 \hfill \cr 0\,\,\,\,\,\,\,\,\,\sqrt 3 \hfill \cr} \right| = - \sqrt 3 \)
\({D_y} = \left| \matrix{ \sqrt 3 \,\,\,\,\,\, - 1 \hfill \cr 2\sqrt 2 \,\,\,\,\,\,0 \hfill \cr} \right| = 2\sqrt 2 \)
Hệ có nghiệm duy nhất:
\(\left\{ \matrix{ x = {{{D_x}} \over D} = \sqrt 3 \hfill \cr y = {{{D_y}} \over D} = - 2\sqrt 2 \hfill \cr} \right.\)