Question

Solve the following pair of linear equations

ax + by = c

bx + ay = 1 + c

Answer 1

ax + by = c … (1)

bx + ay = 1 + c … (2)

Multiplying equation (1) by a and equation (2) by b, we obtain

a²x + aby = ac … (3)

b²x + aby = b + bc … (4)

Subtracting equation (4) from equation (3),

(a² − b²) x = ac − bc − b

 

`x = (c(a-b)-b)/(a^2 - b^2)`

From equation (1), we obtain

ax + by = c

`a{((c(a-b)-b))/(a^2-b^2)}+by = c`

`(ac(a-b)-ab)/(a^2-b^2)+by=c`

`by = c - (ac(a-b)-ab)/(a^2-b^2)`

`by = (a^2c-b^2c-a^2c+abc+ab)/(a^2-b^2)`

`by= (abc-b^2c+ab)/(a^2-b^2)`

`by = (bc(a-b)+ab)/(a^2-b^2)`

`y= (c(a-b)+a)/(a^2-b^2)`