Question

Check whether the following equations are consistent or inconsistent , solve them graphically.
$\frac{4}{3}x+2y=8,2x+3y=12$

Answer 1

$\frac{4}{3}x+2y=8,2x+3y=12$

$\Rightarrow 4x+6y=24,2x+3y=12$

$\Rightarrow 2x+3y=12,2x+3y=12$

$\frac{a_1}{a_2}=\frac{4}{2}=2$ ,

$\frac{b_1}{b_2}=\frac{6}{3}=2$

$\frac{c_1}{c_2}=\frac{24}{12}=2$

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

$\therefore$ the linear equation are consistent

$\therefore$ They have infinite solutions.