Question

Show that the system of equations $6x+5y=11,9x+\frac{15}{2}y=21$ has no solution.

Answer 1

The pair of linear equations has no solution if $\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$

$6x+5y=11,9x+\frac{15}{2}y=21a_1=6,b_1=5,c_1=-11a_2=9,b_2=\frac{15}{2},c_2=-21\frac{a_1}{a_2}=\frac{6}{9}=\frac{2}{3}\frac{b_1}{b_2}=\frac{5}{\frac{15}{2}}=\frac{2}{3}\frac{c_1}{c_2}=\frac{11}{21}$

$\therefore \frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$

so, they are inconsistent means no solution