Question

ax+by=c and cx+dy=e how to solve this equation

Answer 1

I am going to tell you the method of elemination of a variable for solving these equations.

ax+by=c
cx+dy=e

Multiply the first equation with c and the second equation with a and then subtrav one equation from the other. This way the coefficient of x will become same in both the equations, hence on subtraction, x will be eliminated.

(ax+by=c)×c
(cx+dy=e)×a
_____________
acx+bcy=c²
acx+ady=ae
- - -
0 + (bc -ad)y= c²-ae

y = (c²-ae)/(bc -ad)

Now, from any one equation, calculate x in terms of y. From first equation,
x = (c-by)/a

Now, put the value of y obtained above and calculate x.

This is how you can solve a pair of linear equations in two variables by method of elimination.