If (9x - 3y) = 96 and 4x : 3y = 20 : 21, then find the value of (2x² + 3y²).

Correct option is C

Given:
Equation 1: 9x - 3y = 96
Equation 2: $$\frac{4x}{3y} = \frac{20}{21}$$​​
Solution:
From the second equation, find the ratio of x to y:
​$$\frac{x}{y} = \frac{20 × 3}{21 × 4}$$​​
​$$\frac{x}{y} = \frac{60}{84}$$​​
​$$\frac{x}{y} = \frac{5}{7}$$​​
Let x = 5k and y = 7k.
Substitute these into the first equation:
9(5k) - 3(7k) = 96
45k - 21k = 96
24k = 96
k =$$\frac{96}{24}$$​​
k = 4
Now find the actual values of x and y:
x = 5 × 4 = 20
y = 7 × 4 = 28
Now calculate the value of $$2x^2 + 3y^2:$$​​
= $$2(20)^2 + 3(28)^2$$​​
= 2(400) + 3(784)
= 800 + 2352
= 3152
Final Answer
So the correct answer is (c)