Find the value of k under the given condition | vedclass

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(B) For a system of two 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} 
eq

Vedclass · Accepted Answer

$k 
eq -10/3$

Vedclass · Answer

(B) For a system of two linear equations $a_1x + b_1y = c_1$ and $a_2x + b_2y = c_2$ to have a unique solution,the condition is $\frac{a_1}{a_2} 
eq \frac{b_1}{b_2}$.Given equations are $2x - 3y = 1$ and $kx + 5y = 7$.Here,$a_1 = 2, b_1 = -3$ and $a_2 = k, b_2 = 5$.Substituting these values into the condition: $\frac{2}{k} 
eq \frac{-3}{5}$.Cross-multiplying gives: $2 	imes 5 
eq -3 	imes k$,which simplifies to $10 
eq -3k$.Therefore,$k 
eq -\frac{10}{3}$.Thus,the system has a unique solution for all real values of $k$ except $k = -\frac{10}{3}$.

Find the value of $k$ under the given condition for the following pair of linear equations: $2x - 3y = 1$ and $kx + 5y = 7$,such that the system has a unique solution.

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