Exams › JEE Advanced › Maths

What is the nature of the solutions for the equations x + y + z = 3, 2x + 2y + 2z = 7, and x − y + 3z = 3?

1. A single solution where x = 1, y = 1, z = 1
2. An infinite number of solutions
3. No possible solution
4. Does not fall into any of these categories

Correct answer: An infinite number of solutions

Solution

The nature of the solutions for the equations is an infinite number of solutions because the system of equations has infinite solutions due to linear dependence between the equations.

Related JEE Advanced Maths questions

• What is the nature of the solution for the equations x + y + z = 3, 2x + y + 2z = 5, and x − y + 3z = 3?
• Consider the matrix M = [0 1 a; 1 2 3; 3 b 1] and its adjugate adj M = [-1 1 -1; 8 -6 2; -5 3 -1], where a and b are real numbers. Which of the following statements is/are true?
• Given that the 3x3 determinant |x, 2, x; x², x, 6; x, 1, x| equals Ax⁴ + Bx³ + Cx² + Dx + E, find the sum of the digits of the square of (5A + 4B + 3C + 2D + E).
• The determinant with rows (x², (y+z)², yz), (y², (x+z)², zx), (z², (x+y)², xy) is divisible by which of the following?
• Consider the determinant equation: det([[a1 + b1*x, a1*x + b1, c1], [a2 + b2*x, a2*x + b2, c2], [a3 + b3*x, a3*x + b3, c3]]) = 0. Which of the following are possible conditions that guarantee this holds for all choices of ai, bi, ci?
• A is a square matrix of order 4 and B = adj(A), where |B| = 27. Find the value of |A^(-1) * adj(3AB)|.

⚔️ Practice JEE Advanced Maths free + battle 1v1 →