Question

The pair of linear equations $5kx + 3y = 7$ and $4x - 3y = k$ has unique solution, if : (A) $k = 0$ (C) $k 
e -5/4$ (B) $k 
e -4/5$ (D) $k = -4/5$

Accepted Answer

B. For a pair of linear equations $a_1x + b_1y = c_1$ and $a_2x + b_2y = c_2$ to have a unique solution, the condition is $\frac{a_1}{a_2} 
e \frac{b_1}{b_2}$. Given equations are: 1) $5kx + 3y = 7 \Rightarrow a_1 = 5k, b_1 = 3$ 2) $4x - 3y = k \Rightarrow a_2 = 4, b_2 = -3$ Applying the condition: $\frac{5k}{4} 
e \frac{3}{-3}$ $\frac{5k}{4} 
e -1$ $5k 
e -4$ $k 
e -4/5$

Unique Solution of Linear Equations

Explanation

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