Question

Solve the following pair of linear equations by elimination method

$\frac{bx}{a}-\frac{ay}{b}+a+b=0$ and $bx-ay+2ab=0$

• A. $x=-a,y=b$
• B. $x=a,y=ab$
• C. $x=-ab,y=b-a$
• D. $x=1,y=\frac{b}{a}$

Answer 1

The correct option is A $x=-a,y=b$

The equations are

$\frac{bx}{a}-\frac{ay}{b}+a+b=0$ ..........(i)

and $bx-ay+2ab=0$.........(ii)

Multiplying (i) by $a$, we get

$bx-\frac{a^2}{b}y+a^2+ab=0$ ......(iii)

Subtracting (iii) from (ii), we get

$y\left(\frac{ab-a^2}{b}\right)=ab-a^2$

$\Rightarrow y=b$

Substituting $y=b$ in (ii), we have

$bx-ab+2ab=0$

$\Rightarrow bx=-ab$

$\Rightarrow x=-a$

$\therefore (x,y)=(-a,b)$