Question

Question 1(iii)
Do the following pair of linear equations have no solution? Justify your answer.
3x + y – 3 = 0 and 2x + $\frac{2}{3}$ y = 2

Answer 1

$3x+y-3=0and2x+\frac{2}{3}y-2=0Here,a_1=3,b_1=1,c_1=-3a_2=2,b_2=2/3,c_2=-2\frac{a_1}{a_2}=\frac{3}{2}and\frac{b_1}{b_2}=\frac{c_1}{c_2}=\frac{3}{2}\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
Hence, the given pair of linear equations rerpresent coincident lines and thus has infinitely many solutions.