![\left \{ {{2(3x-y)-5=2x-3y} \atop {5-(x-2y)=4y+16}} \right. \Rightarrow \left \{ {{6x-2y-5-2x+3y=0} \atop {5-x+2y-4y-16=0}} \right. \Rightarrow \left \{ {{4x+y-5=0} \atop {-x-2y-11=0}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B2%283x-y%29-5%3D2x-3y%7D+%5Catop+%7B5-%28x-2y%29%3D4y%2B16%7D%7D+%5Cright.+%5CRightarrow+%5Cleft+%5C%7B+%7B%7B6x-2y-5-2x%2B3y%3D0%7D+%5Catop+%7B5-x%2B2y-4y-16%3D0%7D%7D+%5Cright.+%5CRightarrow+%5Cleft+%5C%7B+%7B%7B4x%2By-5%3D0%7D+%5Catop+%7B-x-2y-11%3D0%7D%7D+%5Cright.+)
Умножим второе уравнение на 4 и сложим с первым
![\left \{ {{4x+y-5=0} \atop {-4x-8y-44=0}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B4x%2By-5%3D0%7D+%5Catop+%7B-4x-8y-44%3D0%7D%7D+%5Cright.+)
-7y-49=0 ⇒ -7y=49 ⇒y=- 7
-x=11+2y
x = -11-2y=-11-2·(-7)=-11+14=3
Ответ. (3;-7)
№1
1) 5² * 5⁹ = 5¹¹
2) 2⁸ : 2⁴ = 2⁴
3) (3³)² = 3⁶
4) 4⁸ * 7⁸ = (4 * 7)⁸ = 28⁸
5) (х²)⁵ : х³ = х¹⁰ : х³ = х⁷
№2
1) (5m²y³ + 3m³y² -m) - (3m²y³ +2m + 3m³y²) =
= 5m²y³ + 3m³y² - m - 3m²y³ - 2m - 3m³y² = 2m²y³ - 3m
2) 3x² (b + 2x) - 2x(2b²x + x²) = 3x²b + 6x³ - 4x²b² - 2x³ =
= 3x²b - 4x²b² + 4x³ = x²(3b - 4b² + 4x) = x²(b(3 - 4b) + 4x)
№3
1) (-0.7a³b⁴c²)(-1.8a²bc³) = 1.26(abc)⁵
2)
![(2 m^{2}+ \frac{3}{5} n )( \frac{3}{5} n-2 m^{2} )=( \frac{3}{5}n ) ^{2} -(2m ^{2} ) ^{2} = \frac{9}{25}n ^{2} -4m ^{4}](https://tex.z-dn.net/?f=%282+m%5E%7B2%7D%2B+%5Cfrac%7B3%7D%7B5%7D+n+%29%28+%5Cfrac%7B3%7D%7B5%7D+n-2+m%5E%7B2%7D+%29%3D%28+%5Cfrac%7B3%7D%7B5%7Dn+%29+%5E%7B2%7D+-%282m+%5E%7B2%7D+%29+%5E%7B2%7D+%3D+%5Cfrac%7B9%7D%7B25%7Dn+%5E%7B2%7D++-4m+%5E%7B4%7D+)
3) (18x³y³ - 12x⁴y) : (6x³y) = 3y² - 2x
№4
(b³ - b²)(b³ + b²) - (1 + b²)(1 - b² + b⁴) = b⁶ - b⁴ - 1 + b² - b⁴ - b² + b⁴ - b⁶ =
= - 1 - b⁴ = -(1 + b⁴)
- (1 + 0.1⁴) = - (1 + 0,0001) = - 1,0001
№5
х(х + 2) - (х + 3)(х + 1) = 2х + 3
х² + 2х - х² - х - 3х - 3 = 2х + 3
- х - 3х - 3 = + 3
4х = - 6
х = - 1,5
Ответ: - 1,5.
y=-0.5x+b
-5=-1+b , b=-4
Прямая параллельная заданной и проходящая через заданную точку
y=-0.5x-4