Question

Solving a General System of Equations Find xand yin

terms of aand b.

$\left\{\begin{array}{l}ax+by=0\\ x+y=1\end{array}\right.(a\ne b)$

Short answer

$x=\frac{-b}{a-b}$

$y=\frac{a}{a-b}$

Step-by-step solution

Step 1. Write down the concept.

The given system of equation can be written as,

ax + by = 0 …..(1)

$x+y=1$ …...(2)

Multiplying a to (2), we get

$ay-by=a$ ……(3)

$y=\frac{a}{a-b}$

Substituting y in (2) we get,,

$x+\frac{a}{a-b}=1$

$x=1-\frac{a}{a-b}$

$x=-\frac{b}{a-b}$

$x=\frac{a^2-ab}{a(a^2-b^2)}$