Consider the system of linear equations: x_1 + 2x_2 + x_3 = 3 2x_1 + 3x_2 + x_3 = 3 3x_1 + 5x_2 + 2x_3 = 1 The system has: - Mathematics MCQ AIEEE 2026 | ExamTest.live

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Consider the system of linear equations: x_{1} + 2 x_{2} + x_{3} = 3 2 x_{1} + 3 x_{2} + x_{3} = 3 3 x_{1} + 5 x_{2} + 2 x_{3} = 1 The system has:

Solution & Step-by-step Explanation

Let E_{1}, E_{2}, E_{3} be the equations.Observe that E_{1} + E_{2} : (x_{1} + 2 x_{1}) + (2 x_{2} + 3 x_{2}) + (x_{3} + x_{3}) = 3 + 3 3 x_{1} + 5 x_{2} + 2 x_{3} = 6 .But Equation E_{3} is 3 x_{1} + 5 x_{2} + 2 x_{3} = 1 .Since 6 \neq = 1, the equations are inconsistent.Therefore, the system has no solution.

Try it yourself before checking the explanation above.

Consider the system of linear equations: x_{1} + 2 x_{2} + x_{3} = 3 2 x_{1} + 3 x_{2} + x_{3} = 3 3 x_{1} + 5 x_{2} + 2 x_{3} = 1 The system has:

exactly 3 solutions

a unique solution

no solution

infinite number of solutions

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