Question

Identify whether the pair of linear equations have infinite solutions.
$\frac{5}{15}$ 𝒙 + $\frac{2}{7}$ 𝒚 = 𝟐; $\frac{3}{7}$ 𝒚 = 𝟑−$\frac{3}{6}$ 𝒙

Answer 1

Given equations are:

$\frac{5}{15}x+\frac{2}{7}y=2$ .....(1)

$⟹35x+30y=210$

$\frac{3}{7}y=3-\frac{3}{6}x$ .....(2)

$⟹21x+18y=126$

From the equations (1) and (2), we have

$\frac{a_1}{a_2}=\frac{35}{21}=\frac{5}{3}$

$\frac{b_1}{b_2}=\frac{30}{18}=\frac{5}{3}$

$\frac{c_1}{c_2}=\frac{210}{126}=\frac{70}{42}=\frac{5}{3}$

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

Hence pair of equation has infinitely many solutions.