Question

Решите x^2+2y=12 2x-y=10

Answer 1

Уравнения с двумя переменными имеют беск. множество решений, поэтому можем взять любое значение переменной.
$x^2+2y=12$
Пусть x = 3, тогда:
9 + 2y = 12
2y = 3
y = 1,5
Ответ: (3; 1,5).
2)  2x-y=10
Пусть x = 6, тогда:
12 - y = 10
-y = -2
y = 2 
Ответ: (6; 2).

Answer 2

To solve this system of equations, we can use the method of substitution or elimination. Here, we will use the method of substitution.

From the second equation, we can solve for y:

2x - y = 10

y = 2x - 10

Substitute this expression for y into the first equation:

x^2 + 2y = 12

x^2 + 2(2x - 10) = 12

Simplify and solve for x:

x^2 + 4x - 20 = 0

(x + 5)(x - 4) = 0

x = -5 or x = 4

Now, substitute each value of x into either of the original equations to find the corresponding value of y:

For x = -5:

2(-5) - y = 10

y = -20

So one solution is (-5, -20).

For x = 4:

4^2 + 2y = 12

2y = -12

y = -6

So the other solution is (4, -6).

Therefore, the solutions to the system of equations are (-5, -20) and (4, -6).