Question

solve by cross multiplication method ax+by=c and bx+ay=1+c

Answer 1

Answer:

Step-by-step expla

Answer 2

Answer:

$x = \frac {cb^2 - ca^2 - b^2c + ab - abc} {a(b^2 - a^2)}$

$y = \frac{bc - a- ac}{(b^2 - a^2)}$

Step-by-step explanation:

Given equation,

$a\times{x} + b\times{y} = c$..............equation (1)

$b\times{x} + a\times{y} = 1 + c$...............equation(2)

Multiplying by b in equation 1 and a in equation 2, we get

$ab\times{x} + b^{2}\times{y} =  bc$.....equation(3)

$ab\times{x} + a^{2}\times{y} = a + ac$......equation (4)

subtract equation 3 and 4 ,we get

$b^{2}\times{y} - a^{2}\times{y} = bc - a - ac$

$y\times(b^2 - a^2) = bc - a - ac$

$y = \frac{bc - a- ac}{(b^2 - a^2)}$

Put the value of y in equation (1),

$a\times{x} + b\times\frac{bc - a - ac}{b^2 - a^2}$

$a\times{x} = c - b\times\frac{(bc - a - ac)}{b^2 - a^2}$

$x = \frac {cb^2 - ca^2 - b^2c + ab - abc} {a(b^2 - a^2)}$