Question

# For what values of a and b does the following pair of linear equations have infinite number of solution ?$$2x + 3y = 7, a(x + y ) - b(x - y) = 3a + b -2$$

Solution

## $$2x+3y=7$$$$ax-bx+ay+by=3a+b-2$$(or) $$2x+3y=7$$ …………$$(1)$$$$(a-b)x+(a+b)y=3a+b-2$$ ………….$$(2)$$Given: the pair of linear equations have infinite number of solutions$$\dfrac{2}{a-b}=\dfrac{3}{a-b}=\dfrac{7}{3a+b-2}$$$$\Rightarrow \dfrac{2}{a-b}=\dfrac{3}{a+b}$$$$\dfrac{3}{a+b}=\dfrac{7}{3a+b-2}$$$$\Rightarrow 2a+2b=3a-3b$$$$\Rightarrow -a=-5b$$$$\therefore a=5b$$$$3(3a+b-2)=7(a+b)$$$$9a+3b-6=7a+7b$$$$2a-4b-6=0$$$$a-2b=3$$Put $$a=5b$$ in $$a-2b=3$$ we get$$5b-2b=3$$$$\Rightarrow 3b=3$$or $$b=1$$$$\therefore a=5\times 1=5$$, $$b=1$$Hence $$a=5, b=1$$.Maths

Suggest Corrections

0

Similar questions
View More

People also searched for
View More