[x-2x=2 [3x-y^2=11 2)[x^2-3y=-9 [x+y=3 3)[x^2+xy=2 [y-3x=7

Предыдущий
вопрос Следующий
вопрос

1)
Simplify the first equation: x - 2x = 2
-x = 2
x = -2

Plug in x = -2 into the second equation: 3(-2) - y^2 = 11
-6 - y^2 = 11
-y^2 = 17
y^2 = -17
Since there is no real solution to y^2 = -17, the system of equations is inconsistent and has no solution.

2)
Simplify the first equation: x^2 - 3y = -9
x^2 = 3y - 9

Plug in x^2 = 3y - 9 into the second equation: 3y - 9 + y = 2
4y - 9 = 2
4y = 11
y = 11/4

Plug in y = 11/4 into x^2 = 3y - 9:
x^2 = 3(11/4) - 9
x^2 = 33/4 - 9
x^2 = -15/4
x = ± √(-15)/2
x = ±√15 * i /2

The system has complex solutions: x = ±√15 * i /2, y = 11/4

3)
Simplify the first equation: x^2 + xy = 2
x^2 = 2 - xy

Plug in x^2 = 2 - xy into the second equation: y - 3(2 - xy) = 7
y - 6 + 3xy = 7
3xy = y + 1
y = (1/3)x + 1

Plug y = (1/3)x + 1 into x^2 = 2 - xy:
x^2 = 2 - x((1/3)x + 1)
x^2 = 2 - (1/3)x^2 - x
4/3 x^2 + x - 2 = 0
(4x - 6)(x + 1/3) = 0
x = 3/2, x = -1/3

Plug x = 3/2 into y = (1/3)x + 1:
y = (1/3)(3/2) + 1
y = 1 + 1
y = 2

The solution to the system is x = 3/2, y = 2

Therefore, the solutions to the three systems of equations are:
1) No real solutions
2) x = ±√15 * i /2, y = 11/4
3) x = 3/2, y = 2