If $a - 6b + 6c = 4$ and $6a + 3b - 3c = 50$ , where $a , b$ and $c$ are real numbers, the value of $2a + 3b - 3c$ is

CAT 2025 Slot 1 QA Question 17

Multiple choice (+3 / −1) · Algebra · Linear Equation · Try it, then check the answer and solution below.

CAT 2025 Slot 1QAAlgebra • Linear EquationModerate

a - 6b + 6c = 4

and

6a + 3b - 3c = 50 , where

a , b

and

are real numbers, the value of

2a + 3b - 3c$ is

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⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution

Official Convenor Answer Key: B

Answer and solution

Answer: B) 18

📌 Core Concept

We are given a system of linear equations and need to find the value of a specific linear expression. The governing concept is solving linear systems using substitution or elimination.

🔢 Step-by-Step Solution

Given Equations:

a - 6b + 6c = 4

(1)

6a + 3b - 3c = 50

(2)

Express

a

from Equation (1):

a = 4 + 6b - 6c

Substitute

a

into Equation (2):

6(4 + 6b - 6c) + 3b - 3c = 50

24 + 36b - 36c + 3b - 3c = 50

24 + 39b - 39c = 50

39b - 39c = 26

b - c = \frac{26}{39} = \frac{2}{3}

\[ b = c + \frac{2}{3

CAT 2025 Slot 1 QA Question 17

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