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Linear Equations In Two Variables — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsLinear Equations In Two Variables5 Marks
Question
Solve for x and y:
$\frac{\text{bx}}{\text{a}}-\frac{\text{ay}}{\text{b}}+\text{a}+\text{b}=0,$
$\text{bx}-\text{ay}+\text{2ab}=0$
✓

Answer

$\frac{b x}{a}-\frac{a x}{b}+a+b=0$
By taking L.C.M., we get
$\frac{b^2 x-a^2 y+a^2 b+b^2 a}{a b}=0$
$b^2 x-a^2 y=-a^2 b-b^2 a $
$b x-a y=-2 a b \ldots . . .(2)$
Multiplying (1) by 1 and (2) by a
$b^2 x-a^2 y=-a^2 b-b^2 a \ldots$
$a b x-a^2 b=-2 a^2 b \ldots(4)$
Subtracting (3) from (4)
$\left(a b-b^2\right) x=-2 a^2 b+a^2 b+a b^2$
$b(a-b) x=-a^2 b+a b^2=-a b(a-b)$
$\therefore x=\frac{-a b(a-b)}{b(a-b)}$
$x=-a$
Putting $x=-a$, in (1), we get
$b^2(-a)-a^2 y=-a^2 b-b^2 a$
$-a b^2-a^2 y=-a^2 b-b^2 a$
$-a^2 y=-a^2 b-b^2 a+a b^2$
$-a^2 y=-a^2 b$
$\Rightarrow y=\frac{-a^2 b}{-a^2}=b$
$\therefore$ solution is $x =- a , y = b$

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