1510.
1)
{x/2 - y/3 = 1 |*6
{x/5 - y/4 = - 1 |*20
{3x - 2y = 6
{4x - 5y = -20 ⇒ -5y = -20-4x ⇒ y =(20+4x)/5 ⇒ y= 4 + 0.8x
3x - 2*(4+0.8x) = 6
3x - 8 - 1.6x = 6
1.4x = 6+8
1.4x= 14
x=14/1.4 = 140/14
x= 10
y=4+0.8*10
y=4+8
y= 12
ответ: (10 ; 12)
2)
{x/3 - y/2 = -3 |*6
{x/2 + y/5 = 5 |*10
{2x -3y = -18 ⇒ 2x=-18+3y ⇒ x= (-18+3y)/2 ⇒ x=0.5(-18 +3y) ⇒x=-9+1.5y
{5x +2y = 50
5*(-9 + 1.5y) + 2y = 50
-45 + 7.5y + 2y = 50
9.5y = 50 + 45
9.5y= 95
y=95/9.5 = 950/95
y=10
x= -9 + 1.5*10
x= - 9 + 15
x= 6
ответ: (6;10)
№1511.
1)
{x/10 - y/5 = 0 |*10
{5x/3 - y/6 = 7 |*6
{x - 2y = 0 ⇒ x=2y
{2*5x +y = 42
10 * 2y +y = 42
20y +y = 42
21y = 42
y= 42/21
y= 2
x= 2 * 2
x= 4
ответ: (4 ; 2)
2)
{x/4 +y/8 = 2 |*8
{2x/9 + y/6 = 1 |*18
{2x +y = 16 ⇒ y= 16-2x
{4x + 3y = 18
4x + 3*(16-2x) = 18
4x +48 - 6x = 18
-2x = 18-48
-2x = -30
x= - 30 /(-2)
x= 15
y= 16 - 2*15
y= 16 - 30
y= -14
ответ: (15 ; - 14)
№1512.
1)
{2(x - 2y) = x - 8y
{5(x+y) = 2(x-y) + 10
{2x -4y = x - 8y
{5x +5y = 2x - 2y + 10
{2x - 4y - x +8y=0
{5x +5y -2x +2y =10
{x +4y =0 ⇒ x = -4y
{3x +7y = 10
3 *(-4y) + 7y = 10
-12y + 7y = 10
-5y= 10
y= 10/(-5)
y= - 2
x= -4 * (-2)
x= 8
ответ : (8 ; - 2)
2)
{3(х+4у) -4х = 2(2х+у)
{7(x-5y) +6x=3(x+4y)+27
{3x+12y -4x = 4x +2y
{7x -35y +6x = 3x +12y +27
{-x -4x = 2y -12y
{13x -35y -3x -12y = 27
{ -5x = -10y |: (-5)
{ 10x - 47y = 27
{x=2y
{10x - 47y = 27
10*2y -47y = 27
20y - 47y = 27
-27y = 27
y = -1
x= 2*(-1)
x= -2
ответ: (-2; - 1)