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What is the value of x+y ?

## Value of the variables - Quadratic Equation

If (3x+2y-22)2 + (4x-5y+9)2 = 0 and 5x-4y = 0. Find the value of x+y.
1. 7
2. 9
3. 11
4. 13

Choice B. 9

## Detailed Solution

Do not jump and start expanding the squares.
In equation (1), both the squares will yield either positive number or 0. Since sum of two positive number cannot be 0, each of the term must be 0
∴ 3x + 2y -22 = 0
Multiplying by 2, and adding both equation
6x + 4y - 44 = 0
5x - 4y = 0
=) x = 4
Putting the value of x in the equation
5 x 4 – 4y = 0
y = 5
∴ x+y = 9

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