Question

Dati-mi exemple de sisteme rezolvate prin metoda reducerii.(aproximativ 10)

Answer 1

a.
x+y = 10
x-y = 2
__________
2x / = 12
x = 12/2
x = 6
6 + y = 10
y = 10-6
y = 4

b.
-2x+3y = 4
 2x-5y = 2
__________
/  -2y = 6
y = -6/2
y = -3

-2x + 3 *(-3) = 4
-2x - 9 = 4
-2x = 4 + 9
-2x = 13
2x = -13
x = -13/2

c.
-x-3y = 7  / 2 adica se inmukltestet cu 2
2x+y =8

-2x -6y = 14
2x + y = 8
_________
/  -5y = 22
y = -22/5

-x +3 * 22/5 = 7
-5x + 66 = 35
-5x = 35-66
-5x = -31
x = 31/5

d.
2x+3y = 9 / 4 adica o inmultesti cu 4
5x-4y = 7 / 3, adica o inmultesti cu 3

8x+12y = 36
15x - 12y = 21
______________
23 x /    = 57
x = 57/23

2*57/23 + 3y = 9
2*57 + 3y*23 = 9*23
3y*23 = 207 - 114
3y *23 = 93
y = 93/69

e.
7x - 8y = -45 /13 adica o inmultim cu 13
-15x + 13y = 26 / 8, adica o inmultim cu 8

91 x - 104 y = -585
-120 x + 104y = 208
___________________
-29 x    /      =  -377
x = 377/29
x = 13

7*13 - 8y = -45
91 - 8y = -45
-8y = -45 - 91
-8y = -136
y = 136/8
y = 17

f.
√2 x + √3 y = √8 / -√3
√3 x + √5 y = √12 / √2

-√6 x + 3y =√24
√6 x + √10 y = √24
_____________________
/     3√10y = 2√24
y = (2√24) / 3√10
y = (2√24 * √10) / 3*10
y = (8√15)/30
y = (4 √15) / 15

√2 x + (√3 * 4√15)/15 = √8
√2 x + (12√5)/15 = √8
15√2 x + 12√5 = √8
15√2 x = √8 - 12√5
x = (√8 - 12√5) /15√2
x = √2(√8 - 12√5) /30