№ 1035(в)
{2x - 4y = 5 ⇒ x= (5 +4y)/2 = ¹/₂ × (5 + 4y) = 2.5 + 2y
{4x - 3y = 5
4×(2.5 + 2y) - 3y = 5
10 + 8y - 3y = 5
10 + 5y = 5
5y = 5 - 10
5y = - 5
y = - 1
x = 2.5 + 2*(-1) = 2.5 - 2
x = 0.5
Ответ : ( 0.5 ; - 1) .
№1036
а)
{ 6x + y = 1
{ 3x - y = 8
6x + y + 3x - y = 1 + 8
(6х + 3х) + (у - у) = 9
9x = 9
x = 1
6×1 +y = 1
y = 1 - 6
y = - 5
Ответ : ( 1 ; - 5) .
б)
{ 3x - 4y = 9
{ 3x + 2y = - 9 |×2
3x - 4y + 2(3x + 2y) = 9 + (-9)×2
3x - 4y + 6x + 4y = 9 - 18
9x = - 9
x = - 1
3×(-1) - 4y = 9
- 3 - 4y = 9
- 4y = 9 + 3
- 4y = 12
y = 12 : ( - 4)
у = - 3
Ответ : ( - 1 ; - 3) .
в)
{5x - 7y = 1 | × 5
{6x - 5y = 8 | × ( - 7)
5(5x - 7y) + (-7)(6x - 5y) = 1×5 + 8×(-7)
25x - 35y - 42x + 35y = 5 - 56
- 17x = - 51 | × ( - 1)
17x = 51
x = 51 : 17
х = 3
5 × 3 - 7у = 1
15 - 7у = 1
- 7у = 1 - 15
- 7у = - 14 | : ( - 7)
у = 2
Ответ : ( 3 ; 2) .