Question

# Solve the following pair of equations by cross- multiplication method:$$2ax + 3by = a + 2b$$$$3ax + 2by = 2a + b$$

Solution

## $$2ax + 3by = a + 2b$$$$3ax + 2by = 2a + b$$Give, pair of equations is$$2ax + 3by = a + 2b \Rightarrow 2ax + 3by - (a + 2b) = 0$$$$3ax + 2by = 2a + b \Rightarrow 3ax + 2by - (2a + b) = 0$$By cross-multiplication method, we have $$\Rightarrow \frac{x}{-3ab(2a + b) + 2b(a + 2b)} = \frac{y}{-3a(a + 2b) + 2a(2a + b)} = \frac{1}{4ab - 9ab}$$ $$\Rightarrow \frac{x}{-4ba - 3b^2 + 4ab + b^2} = \frac{y}{-3a^2 - 6ba + 4a^2 + 2ab} = \frac{1}{-5ab}$$$$\Rightarrow \frac{x}{b^2 - 4ab} = \frac{y}{-4ab + a^2} = \frac{1}{-5ab}$$            I                II               IIIOn taking I and III ratio, we get $$\Rightarrow \frac{x}{b^2 - 4ab} = \frac{1}{-5ab}$$$$\Rightarrow x = \frac{b(b - 4a)}{5a}$$$$\Rightarrow \frac{4a - b}{5a}$$On taking II and III ratio, we get$$\Rightarrow \frac{y}{-4ab + a^2} = \frac{1}{-5ab}$$$$\Rightarrow y = \frac{a(a - 4b)}{-5ab}$$$$\Rightarrow y = \frac{4b - a}{5b}$$Mathematics

Suggest Corrections

0

Similar questions
View More

People also searched for
View More