5x-3y =9 and xy =-7, then the value of 25x2 + 9y?

Answer 1

First, let's find the values of x and y by solving the two given equations:

5x - 3y = 9
xy = -7

From the second equation, we can write x in terms of y:
x = -7/y

Substitute x = -7/y into the first equation:
5(-7/y) - 3y = 9
-35/y - 3y = 9
-35 - 3y^2 = 9y
3y^2 + 9y - 35 = 0

Solving for y by factoring the quadratic equation:
(3y - 5)(y + 7) = 0
y = 5/3 or y = -7

If y = 5/3, then x = -7/(5/3) = -21/5
If y = -7, then x = -7/(-7) = 1

Now, we can find the value of 25x^2 + 9y:

When y = 5/3 and x = -21/5:
25(-21/5)^2 + 9(5/3) = 25(441/25) + 15 = 441 + 15 = 456

When y = -7 and x = 1:
25(1)^2 + 9(-7) = 25 + (-63) = -38

Therefore, the value of 25x^2 + 9y can be either 456 or -38, depending on the values of x and y.