Bài 12 trang 75 Sách bài tập (SBT) Toán Đại số 10

Giải các hệ phương trình

a) \(\left\{ \matrix{5x + 3y = - 7 \hfill \cr 2x - 4y = 6 \hfill \cr} \right.\)

b) \(\left\{ \matrix{7x + 14y = 17 \hfill \cr 2x + 4y = 5 \hfill \cr} \right.\)

c) \(\left\{ \matrix{
{2 \over 5}x + {3 \over 7}y = {1 \over 3} \hfill \cr
{5 \over 3}x - {5 \over 7}y = {2 \over 3} \hfill \cr} \right.\)

d) \(\left\{ \matrix{
- 0,2x + 0,5y = 1,7 \hfill \cr
0,3x - 0,4y = 0,9 \hfill \cr} \right.\)

Gợi ý làm bài

a) 

\(\eqalign{
& \left\{ \matrix{
5x + 3y = - 7 \hfill \cr
2x - 4y = 6 \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{
10x + 6y = - 14 \hfill \cr
10x - 20y = 30 \hfill \cr} \right. \cr
& \Leftrightarrow \left\{ \matrix{
5x + 3y = - 7 \hfill \cr
26y = - 44 \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{
x = - {5 \over {13}} \hfill \cr
y = - {{22} \over {13}} \hfill \cr} \right. \cr} \)

b)

\(\left\{ \matrix{
7x + 14y = 17 \hfill \cr
2x + 4y = 5 \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{
14x + 28y = 34 \hfill \cr
14x + 28y = 35 \hfill \cr} \right. \Rightarrow \) Hệ phương trình vô nghiệm.

c) 

\(\eqalign{
& \left\{ \matrix{
{2 \over 5}x + {3 \over 7}y = {1 \over 3} \hfill \cr
{5 \over 3}x - {5 \over 7}y = {2 \over 3} \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{
2x + {{15} \over 7}y = {5 \over 3} \hfill \cr
5x - {{15} \over 7}y = 2 \hfill \cr} \right. \cr
& \Leftrightarrow \left\{ \matrix{
7x = {{11} \over 3} \hfill \cr
2x + {{15} \over 7}y = {5 \over 3} \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{
x = {{11} \over {21}} \hfill \cr
y = {{13} \over {45}} \hfill \cr} \right. \cr} \)

d) 

\(\eqalign{
& \left\{ \matrix{
- 0,2x + 0,5y = 1,7 \hfill \cr
0,3x + 0,4y = 0,9 \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{
- 0,6x + 1,5y = 5,1 \hfill \cr
0,6x + 0,8y = 1,8 \hfill \cr} \right. \cr
& \Leftrightarrow \left\{ \matrix{
2,3y = 6,9 \hfill \cr
0,3x + 0,4y = 0,9 \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{
x = - 1 \hfill \cr
y = 3 \hfill \cr} \right. \cr} \)

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