Решаем:
а) 2x + 3y = 16
3x - 2y = 11
Из 1-го ур-ния y = (16 - 2x) / 3
Подставляем во 2-е
3x - 2*(16 - 2x) / 3 = 11
9x - 32 + 4x = 33
13x = 65, x = 5, y = (16 - 2x) / 3 = 2
ответ: x = 5, y = 2
б) 6(x + y) = 5 - (2x + y)
3x - 2y = -3 (или -3 -3 = -6, уточни)
Из 2-го у = (3х + 3) / 2
6(x + (3х + 3) / 2) = 5 - (2x + (3х + 3) / 2)
6(5x + 3) / 2 = 5 - (7x + 3) / 2
6(5x + 3) = 10 - (7x + 3)
30x + 18 = 10 - 7x - 3
37x = -11, x = -11/37, y = (3х + 3) / 2 = (-33+111) / (2*37) = 78 / (2*37) = 39/37
ответ: x = -11/37, y = 39/37
в) 2x + 3y = 3
5x - 4y = 19
y = (3 - 2x) / 3
5x - 4(3 - 2x) / 3 = 19
15x - 12 + 8x = 57
23x = 69, x = 3
y = (3 - 2x) / 3 = (3 - 6) / 3 = -1
ответ: x = 3, y = -1
г) 3x + 2y = 6
5x + 6y = -2
y = (6 - 3x) / 2
5x + 6(6 - 3x) / 2 = -2
5x + 3(6 - 3x) = -2
5x + 18 - 9x = -2
4x = 20, x = 5
y = (6 - 3x) / 2 = (6 - 15) / 2 = -9/2
ответ: x = 5, y = -4,5
Подробнее - на -
a)5(x+1)-x>2(x+1) c)5x(2x+1)<10x(x+1)-1 e)(b-1)(b+1)≤b(b+2)
5x+5-x>2x+2 10x²+5x<10x²+10x-1 b²-1≤b²+2b
4x+5>2x+2 10x²+5x-10x²+10x+1<0 b²-1-b²+2b≤0
4x+5-2x-2>0 15x+1<0 -1+2b≤0
2x+3>0 15x<-1 2b≤1
2x>-3 x<-1/15 b≤0,5
x>-1,5 x∈(-∞;-1/15) b∈(-∞;0,5]
x∈(-1,5;+∞)
f)(k+2)(k-3)≥k(k+4)
k²-3k+2k-6≥k²+4k
k²-k-6≥k²+4k
k²-k-6-k²+4k≥0
3k-6≥0
3k≥6
k≥2
x∈[2;+∞)
Решаем:
а) 2x + 3y = 16
3x - 2y = 11
Из 1-го ур-ния y = (16 - 2x) / 3
Подставляем во 2-е
3x - 2*(16 - 2x) / 3 = 11
9x - 32 + 4x = 33
13x = 65, x = 5, y = (16 - 2x) / 3 = 2
ответ: x = 5, y = 2
б) 6(x + y) = 5 - (2x + y)
3x - 2y = -3 (или -3 -3 = -6, уточни)
Из 2-го у = (3х + 3) / 2
6(x + (3х + 3) / 2) = 5 - (2x + (3х + 3) / 2)
6(5x + 3) / 2 = 5 - (7x + 3) / 2
6(5x + 3) = 10 - (7x + 3)
30x + 18 = 10 - 7x - 3
37x = -11, x = -11/37, y = (3х + 3) / 2 = (-33+111) / (2*37) = 78 / (2*37) = 39/37
ответ: x = -11/37, y = 39/37
в) 2x + 3y = 3
5x - 4y = 19
y = (3 - 2x) / 3
5x - 4(3 - 2x) / 3 = 19
15x - 12 + 8x = 57
23x = 69, x = 3
y = (3 - 2x) / 3 = (3 - 6) / 3 = -1
ответ: x = 3, y = -1
г) 3x + 2y = 6
5x + 6y = -2
y = (6 - 3x) / 2
5x + 6(6 - 3x) / 2 = -2
5x + 3(6 - 3x) = -2
5x + 18 - 9x = -2
4x = 20, x = 5
y = (6 - 3x) / 2 = (6 - 15) / 2 = -9/2
ответ: x = 5, y = -4,5
Подробнее - на -
a)5(x+1)-x>2(x+1) c)5x(2x+1)<10x(x+1)-1 e)(b-1)(b+1)≤b(b+2)
5x+5-x>2x+2 10x²+5x<10x²+10x-1 b²-1≤b²+2b
4x+5>2x+2 10x²+5x-10x²+10x+1<0 b²-1-b²+2b≤0
4x+5-2x-2>0 15x+1<0 -1+2b≤0
2x+3>0 15x<-1 2b≤1
2x>-3 x<-1/15 b≤0,5
x>-1,5 x∈(-∞;-1/15) b∈(-∞;0,5]
x∈(-1,5;+∞)
f)(k+2)(k-3)≥k(k+4)
k²-3k+2k-6≥k²+4k
k²-k-6≥k²+4k
k²-k-6-k²+4k≥0
3k-6≥0
3k≥6
k≥2
x∈[2;+∞)