Question

EXERCISE 3.6
1. Solve the following pairs of equations by reducing them to a pair of linear equations:
6x+3y=6xy​

Answer 1

Step-by-step explanation:

given equation,

6x+3y=6xy .....(1)

2x+4y=5xy ......(2)

divide the terms by xy

6x/xy +3y/xy =6xy/xy

2x/xy +4y/xy =5xy/xy

the new equation will be,

6/y + 3/x = 6

2/y + 4/x =5

let (1/y) be (a) and (1/x) be (b)

6a + 3b = 6

3(2a+b)=6

2a+ b = 2 .........(3)

2a + 4b = 5 .........(4)

by equation (3)and (4),we get

2a + b = 2

2a + 4b = 5

(-) (-) (-)

by elimination we get ( b=1)

now,putting the value of b in equation (3)

2a+b = 2

2a +1=2

2a=2-1

2a=1

a=1/2

comparing the equation,we get

(1/x)=1 , (1/y)= (1/2)

x= 1 y= 2

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