Bài tập 5 trang 70 SGK Đại số 10

Bài tập 5 trang 70 SGK Đại số 10

Câu a:

Ta có:  \(D = \left| \begin{array}{l} - 2\,\,\,\,\,\,\,\,\,5\\4\,\,\,\,\,\,\,\,\,\,\,\,\,2\end{array} \right|\,\, =  - 24 \ne 0\)

\(Dx = \left| \begin{array}{l}9\,\,\,\,\,\,\,\,\,\,\,\,\,\,5\\11\,\,\,\,\,\,\,\,\,\,2\end{array} \right| = 9.2 - 11.5 =  - 37\)

\(Dy = \left| \begin{array}{l} - 2\,\,\,\,\,\,\,\,\,\,9\\4\,\,\,\,\,\,\,\,\,\,\,11\end{array} \right| =  - 2.11 - 4.9 =  - 58\)

\( \Rightarrow \) hệ có nghiệm: \(\left\{ \begin{array}{l}x = \frac{{Dx}}{D} = \frac{{ - 37}}{{ - 24}} = \frac{{37}}{{24}}\\y = \frac{{Dy}}{D} = \frac{{ - 58}}{{ - 24}} = \frac{{29}}{{12}}\end{array} \right.\)

Vậy hệ phương trình có nghiệm: \(\left\{ \begin{array}{l}x = \frac{{37}}{{24}}\\y = \frac{{29}}{{12}}\end{array} \right.\)

Câu b:

Ta có: \[D = \left| \begin{array}{l}3\,\,\,\,\,\,\,\,\,4\\5\,\,\,\,\, - 2\end{array} \right|\,\, = 3.( - 2) - 5.4 =  - 26 \ne 0\]

\(Dx = \left| \begin{array}{l}12\,\,\,\,\,\,\,\,\,4\\7\,\,\,\,\,\,\,\, - 2\end{array} \right|\,\, =  - 2.12 - 7.4 =  - 52\)

\(Dy = \left| \begin{array}{l}3\,\,\,\,\,\,\,\,\,12\\5\,\,\,\,\,\,\,\,\,\,\,\,\,7\end{array} \right|\,\, = 3.7 - 5.12 =  - 39\)

\( \Rightarrow \) hệ có nghiệm: \(\left\{ \begin{array}{l}x = \frac{{Dx}}{D} = \frac{{ - 52}}{{ - 26}} = 2\\y = \frac{{Dy}}{D} = \frac{{ - 39}}{{ - 26}} = \frac{3}{2}\end{array} \right.\)

Vậy hệ phương trình có nghiệm: \(\left\{ \begin{array}{l}x = 2\\y = \frac{3}{2}\end{array} \right.\)

Câu c:

Ta có: \[D = \left| \begin{array}{l}2\,\,\,\,\,\,\,\,\, - 3\\3\,\,\,\,\,\,\,\,\,\,\,\,\,2\end{array} \right|\,\, = 2.2 - 3.( - 3) = 13\]

\(Dx = \left| \begin{array}{l}5\,\,\,\,\, - 3\\8\,\,\,\,\,\,\,\,\,\,2\end{array} \right|\,\, = 2.5 - 8.( - 3) = 34\)

\(Dy = \left| \begin{array}{l}2\,\,\,\,\,\,\,\,\,\,\,\,\,5\\3\,\,\,\,\,\,\,\,\,\,\,\,\,8\end{array} \right|\,\, = 2.8 - 3.5 = 1\)

\( \Rightarrow \) hệ có nghiệm: \(\left\{ \begin{array}{l}x = \frac{{Dx}}{D} = \frac{{34}}{{13}}\\y = \frac{{Dy}}{D} = \frac{1}{{13}}\end{array} \right.\)

Vậy hệ phương trình có nghiệm: \(\left\{ \begin{array}{l}x = \frac{{34}}{{13}}\\y = \frac{1}{{13}}\end{array} \right.\)

Câu d:

Ta có: \[D = \left| \begin{array}{l}5\,\,\,\,\,\,\,\,\,3\\4\,\,\,\,\, - 5\end{array} \right|\,\, = 5.( - 5) - 4.3 =  - 37 \ne 0\]

\(Dx = \left| \begin{array}{l}15\,\,\,\,\,\,\,\,\,3\\6\,\,\,\,\,\,\,\, - 5\end{array} \right|\,\, =  - 5.16 - 6.3 =  - 93\)

\(Dy = \left| \begin{array}{l}5\,\,\,\,\,\,\,\,\,15\\4\,\,\,\,\,\,\,\,\,\,\,\,\,6\end{array} \right|\,\, = 5.6 - 4.15 =  - 30\)

\( \Rightarrow \) hệ có nghiệm: \(\left\{ \begin{array}{l}x = \frac{{Dx}}{D} = \frac{{ - 93}}{{ - 37}} = \frac{{93}}{{37}}\\y = \frac{{Dy}}{D} = \frac{{ - 30}}{{ - 37}} = \frac{{30}}{{37}}\end{array} \right.\)

Vậy hệ phương trình có nghiệm: \(\left\{ \begin{array}{l}x = \frac{{93}}{{37}}\\y = \frac{{30}}{{37}}\end{array} \right.\)

-- Mod Toán 10