GATE XE (Engineering Sciences) 2025 - Question 20

Section: Engineering Mathematics | Type: MSQ | Marks: 2

For 𝑎, 𝑏∈ℝ, consider the system of linear equations 𝑥+ 𝑦+ 𝑎𝑧= 2 2𝑦+ 2𝑧= 1 𝑎𝑥+ 2𝑧= 𝑏 If the system has infinitely many solutions, then which of the following statements is/are correct ?

• A. 𝑎= 2, 𝑏= 3
• B. 𝑎= 2, 𝑏= 5
• C. 𝑎= −1, 𝑏= − 3 2
• D. 𝑎= 3, 𝑏= 5

Answer: A. 𝑎= 2, 𝑏= 3; C. 𝑎= −1, 𝑏= − 3 2