Giải hệ phương trình

To solve the system of equations:

a) √(3x) + y = 7
2x - √(3y) = -2√3

b) x - 2y
----- + ----- = -1
5 3

3x - 5y = 51

We can start by solving equation a) for y:

√(3x) = 7 - y
3x = (7 - y)^2
3x = 49 - 14y + y^2

Now, we can substitute this expression for 3x in equation b):

2(49 - 14y + y^2) - √(3y) = -2√3

98 - 28y + 2y^2 - √(3y) = -2√3

Rearranging the terms:

2y^2 - 28y + √(3y) - 2√3 + 98 = 0

This is a quadratic equation in terms of y. We can solve it using the quadratic formula:

y = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 2, b = -28, and c = -2√3 + 98.

Solving for y, we get two possible values.

Once we have the values of y, we can substitute them back into equation a) to solve for x.

Finally, we can substitute the values of x and y into equation 3x - 5y = 51 to check if they satisfy the third equation.