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Giải các hệ phương trình
a) \(\left\{ \matrix{
– 7x + 3y = – 5 \hfill \cr
5x – 2y = 4; \hfill \cr} \right.\)
b) \(\left\{ \matrix{
4x – 2y = 6 \hfill \cr
– 2x + y = – 3 \hfill \cr} \right.\)
c) \(\left\{ \matrix{
– 0,5x + 0,4y = 0,7 \hfill \cr
0,3x – 0,2y = 0,4; \hfill \cr} \right.\)
d) \(\left\{ \matrix{
{3 \over 5}x – {4 \over 3}y = {2 \over 5} \hfill \cr
– {2 \over 3}x – {5 \over 9}y = {4 \over 3}; \hfill \cr} \right.\)
Gợi ý làm bài
a)
\(\eqalign{
& \left\{ \matrix{
– 7x + 3y = – 5 \hfill \cr
5x – 2y = 4 \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{
– 14x + 6y = – 10 \hfill \cr
15x – 6y = 12 \hfill \cr} \right. \cr
& \Leftrightarrow \left\{ \matrix{
x = 2 \hfill \cr
5x – 2y = 4 \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{
x = 2 \hfill \cr
y = 3 \hfill \cr} \right. \cr} \)
b)
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\(\eqalign{
& \left\{ \matrix{
4x – 2y = 6 \hfill \cr
– 2x + y = – 3 \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{
2x – y = 3 \hfill \cr
2x – y = 3 \hfill \cr} \right. \cr
& \Leftrightarrow 2x – y = 3 \cr} \)
Vậy hệ phương trình có vô số nghiệm \((x;y) = (a;2a – 3)\), a tùy ý.
c)
\(\eqalign{
& \left\{ \matrix{
– 0,5x + 0,4y = 0,7 \hfill \cr
0,3x – 0,2y = 0,4 \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{
– 0,5x + 0,4y = 0,7 \hfill \cr
0,6x – 0,4y = 0,8 \hfill \cr} \right. \cr
& \Leftrightarrow \left\{ \matrix{
x = 15 \hfill \cr
0,3x – 0,2y = 0,4 \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{
x = 15 \hfill \cr
y = 20,5 \hfill \cr} \right. \cr} \)
d)
\(\eqalign{
& \left\{ \matrix{
{3 \over 5}x – {4 \over 3}y = {2 \over 5} \hfill \cr
– {2 \over 3}x – {5 \over 9}y = {4 \over 3} \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{
{3 \over 5}x – {4 \over 3}y = {2 \over 5} \hfill \cr
– {3 \over 5}x – {1 \over 2}y = {6 \over 5} \hfill \cr} \right. \cr
& \Leftrightarrow \left\{ \matrix{
– {{11} \over 6}y = {8 \over 5} \hfill \cr
{3 \over 5}x – {4 \over 3}y = {2 \over 5} \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{
x = – {{14} \over {11}} \hfill \cr
y = – {{48} \over {55}} \hfill \cr} \right. \cr} \)