Question

Which of the following is true if following pair of equations has unique solution? 3x – 2y = - 8 and (2m – 5)x + 7y – 6 = 0 *​

Answer 1

Answer:

3/(2m-5)=-2/7

21=-2(2m-5)

21=-4m+10

11=-4m

m=-11/4

Answer 2

Given,

The first equation$\[ = 3x - 2y + 8\]$

The second equation$\[ = \left( {2m - 5} \right)x + 7y - 6\]$

To find,

The condition for the unique solution for the pair of equations.

Solution,

Know that for a pair of equations$\[\left( {{a_1}x + {b_1}y + {c_1} = 0,{a_2}x + {b_2}y + {c_2} = 0} \right)\]$ to have a unique solution, the following condition must be satisfied,

$\[ \Rightarrow \frac{{{a_1}}}{{{a_2}}} \ne \frac{{{b_1}}}{{{b_2}}}\]$

Apply values.

Therefore,

$\[\begin{array}{l} \Rightarrow \frac{3}{{2m - 5}} \ne \frac{{ - 2}}{7}\\ \Rightarrow - 4m + 10 \ne 21\\ \Rightarrow 4m \ne 10 - 21\end{array}\]$

Solve further,

$\[\begin{array}{l} \Rightarrow 4m \ne - 11\\ \Rightarrow m \ne - \frac{{11}}{4}\end{array}\]$

Hence, the condition for the unique solution for the pair of equations is$\[m \ne - \frac{{11}}{4}.\]$