CAT Quantitative Aptitude Questions | CAT Algebra - Linear Equations; Quadratic Equations

The question is about finding Value of variables of a Quadratic Equation. Two different equations involving two variables are given and we need to find out x + y. Framing and solving equations is an integral part of Linear Equations and Quadratic Equations. Get as much practice as you can in these two topics because the benefits of being good at framing equations will be useful in other concepts.

Question 13: 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

Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Quadratic Equations: What is the value of x+y ?

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

The question is "If (3x+2y-22)² + (4x-5y+9)² = 0 and 5x-4y = 0. Find the value of x+y?"

Hence the answer is "9"

Choice B is the correct answer.