Question

Does the following pair of linear equations have a unique solution?
$7x+2y=21$
$21x+6y=63$

• A. yes
• B. no

Answer 1

The correct option is B no

Given pair of equations
$7x+2y=21\dots \left(i\right)$
$21x+6y=63\dots \left(ii\right)$

Equation$\left(i\right)\Rightarrow y=-\frac{7x}{2}+\frac{21}{2}\dots \left(iii\right)$

Equation $\left(ii\right)\Rightarrow$ Divide both the sides on equation by $3,$ we get
$\Rightarrow \frac{1}{3}(21x+6y)=\frac{1}{3}\times 63$
$\Rightarrow 7x+2y=21\Rightarrow y=-\frac{7x}{2}+\frac{21}{2}\dots \left(iv\right)$

Slope of line, $\left(iii\right)=-\frac{7}{2},and$ intercept of line, $\left(iii\right)=\frac{21}{2}$
Slope of line, $\left(iv\right)=-\frac{7}{2},and$ intercept of line, $\left(iv\right)=\frac{21}{2}$

As, line $\left(i\right)$ and $\left(ii\right)$ are having same slope and intercepts. So both the lines are identical and intersect at infinite many points.
$\therefore$ Given pair of equations have infinite many solution