Question

For what value of μ do the simultaneous equations 5x + 7y = 2, 15x + 21y = μ have no solution?
1. μ = 0
2. μ ≠ 6
3. μ ≠ 0
4. μ = 6

Answer 1

Correct Answer - Option 2 : μ ≠ 6

Concept:

System of equations

a₁x + b₁y = c₁

a₂x + b₂y = c₂

For unique solution

\(\frac {a_1}{a_2}≠ \frac {b_1}{b_2}\)

For Infinite solution

\(\frac {a_1}{a_2}= \frac {b_1}{b_2}= \frac {c_1}{c_2}\)

For no solution

\(\frac {a_1}{a_2}=\frac {b_1}{b_2}≠ \frac {c_1}{c_2}\)

Calculation:

Given:

5x + 7y = 2, 15x + 21y = μ

Here For no solution

\(\frac 5{15}=\frac 7{21}≠ \frac 2{μ}\)

Hence for no solution μ ≠ 6