Question

Question 7 (ii)
Solve the following pair of linear equations.
(ii) ax + by = c
bx + ay = 1 + c

Answer 1

$\left(ii\right)ax+by=c\cdots \left(1\right)bx+ay=1+c\cdots \left(2\right)$
Multiplying equation (1) by a and equation (2) by b, we obtain
$a^{2}x+aby=ac\cdots \left(3\right)b^{2}x+aby=b+bc\cdots \left(4\right)$
Subtracting equation (4) from equation (3),
$(a^2-b^2)x=ac-bc-b$
$x=\frac{c(a-b)-b}{a^2-b^2}$
From equation (1), we obtain
$ax+by=ca\left\{\frac{c(a-b)-b}{a^2-b^2}\right\}+by=c\frac{ac(a-b)-ab}{a^2-b^2}+by=cby=c-\frac{ac(a-b)-ab}{a^2-b^2}by=\frac{a^{2}c-b^{2}c-a^{2}c+abc-ab}{a^2-b^2}by=\frac{abc-b^{2}c-ab}{a^2-b^2}by=\frac{b\left(\right(ca-bc)-a)}{a^2-b^2}y=\frac{c(a-b)-a}{a^2-b^2}$