Question

Solve : ax +by +-c =0
bx+ ay=1+c

Answer 1

According to the question,

we have, $ax+by=c,bx+ay=1+c$

suppose......

$ax+by=c,$ -----------(1)

$bx+ay=1+c$------------(2)

(for finding the y co-ordinate),

multiply by b into equation-------------(1)

$abx+b^{2}y=bc$------A

multiply by a into equation------------(2)

$abx+a^{2}y=a+ac$-------B

then,subtracting into equ A &B,$$\begin{array}{c}\underset{–}{\begin{array}{c}abx+b^{2}y=bc\\ {abx}_{-}{+}_{-}{a}^{2}y=a_{-}+a_{-}c\end{array}}\\ y(b^2-a^2)=bc-a-ac\\ y=\frac{c(b^2-a^2)-a}{b^2-a^2}\end{array}$$

And, (for finding the x co-ordinate),

multiply by a into equation-------------(1)

$a^{2}x+aby=ac$------------A

multiply by b into equation-------------(2)

$b^{2}x+aby=b+bc$-------------B

then, subtracting into equ A & B,

$$\begin{array}{c}\underset{–}{\begin{array}{c}{a}^{2}x+aby=ac\\ {b^{2}x}_{-}{+}_{-}aby=b_{-}+b_{-}c\end{array}}\\ x(a^2-b^2)=ac-b-bc\\ x=\frac{c(a-b)-b}{a^2-b^2}\end{array}$$

So, we have x and y value.