Question:medium

The system of equations:
\[ x - y + 2z = 4 \] \[ 3x + y + 4z = 6 \] \[ x + y + z = 1 \] has:

Show Hint

If \( \Delta = 0 \) and all augmented determinants are also zero, the system has infinitely many solutions.

Updated On: Nov 26, 2025

unique solution
infinitely many solutions
no solution
two solutions

Top Questions on Algebra

If $ x + \frac{1}{x} = 2 \cos \theta $, find the value of \[ x^5 + \frac{1}{x^5} \] in terms of $\theta$.
- BITSAT - 2025
- Mathematics
- Algebra
View Solution
From the top of a 50 m tall building, the angles of depression to two points on the ground are \( 45^\circ \) and \( 30^\circ \). Find the distance between the two points.
- BITSAT - 2025
- Mathematics
- Algebra
View Solution
Maximize \( z = 5x + 2y \) subject to \( 2x + y \leq 8 \), \( x \geq 0 \), \( y \geq 0 \). What is the maximum value of \( z \)?
- BITSAT - 2025
- Mathematics
- Algebra
View Solution
If the word "BITS" is coded using \( A=1, B=2, \ldots, Z=26 \), and the code is the sum of the squares of each letter's value, what is the code for the word?
- BITSAT - 2025
- Mathematics
- Algebra
View Solution
Want to practice more? Try solving extra ecology questions todayView All Questions

Questions Asked in BITSAT exam

A sequence is defined as follows: \( a_1 = 1, a_2 = 2 \), and \( a_n = a_{n-1} + a_{n-2} \) for \( n \geq 3 \). What is the 6th term of the sequence?

BITSAT - 2025
Sequence and Series

View Solution

Choose the word closest in meaning to 'Candid'.

BITSAT - 2025
Vocabulary

View Solution

What is the sum of the first 10 terms of the arithmetic progression with first term 3 and common difference 2?

BITSAT - 2025
Arithmetic Progression

View Solution

In the reaction \( 2\text{SO}_2 + \text{O}_2 \rightarrow 2\text{SO}_3 \), if 64 g of \(\text{SO}_2\) reacts completely, how many grams of \(\text{SO}_3\) are produced? (Molar mass of \(\text{SO}_2 = 64 \, \text{g/mol}, \text{SO}_3 = 80 \, \text{g/mol}\))

BITSAT - 2025
Stoichiometry and Stoichiometric Calculations

View Solution