Question

Does the following pair of linear equations have a unique solution?
$2x+3y=6$
$y=\left(\frac{-2}{3}\right)x+\frac{5}{6}$

• A. yes
• B. no

Answer 1

The correct option is B no

Given pair of lines
$2x+3y=6$ $\dots \left(1\right)$
$y=\left(\frac{-2}{3}\right)x+\frac{5}{6}$ $\dots \left(2\right)$

Equation ($1$) $\Rightarrow 3y=-2x+6$
Divide both the sides by $3$
$\Rightarrow \frac{3y}{3}=\frac{-2}{3}x+\frac{6}{3}$
$\Rightarrow y=\left(\frac{-2}{3}\right)x+2\dots \left(3\right)$
and $y=\left(\frac{-2}{3}\right)x+\frac{5}{6}\dots \left(2\right)$
As, slopes of both the lines is $-\frac{2}{3},$ so both lines are parallel.
Hence, given pair of equations have no solution.