Question

ax + by = c
x + by = d​

Answer 1

$\huge \orange{ \overbrace{ \red{\underbrace \color{blue} {\underbrace \color{black}{\colorbox{lime}{ {\red \: {☘Answer ☘ }}}}}}}}$

✪QUESTION✪:-

ax + by = c

x + by = d

find x and y.

✪ANSWER✪:-

ax + by = c

x + by = d

__________

➠ax-x = c-d

➠(a-1) x = c-d

➠$x = \frac{c - d}{a - 1}$

sub/: $x = \frac{c - d}{a - 1}$ in first equation,

➠ax + by = c

➠a$( \frac{c - d}{a - 1} )$+ by = c

➠$\frac{ac -ad}{a - 1}$+ by = c

➠$\frac{(ac -ad)- (a - 1)by}{(a - 1)} = c$

➠ac-ad- (ab-b)y = c(a-1)

➠ac-ad-(ab-b)y = ac -c

➠-(ab-b)y = ac-c -ac+ad

➠-(ab-b)y = ad-c

➠ $y = - \frac{ad - c}{ab - b}$