Question

5. Solve the equation: 6x+3y=6xy and 2x+4y=5xy
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Answer 1

Answer:

6x+3y-6x-12y= 6xy-15xy

-9y=-9xy

X=1

for y

6*1= 6y-3y=3y

3y=6

y=2

Answer 2

SOLUTION:-

Given

• 6x+3y=6xy

• 2x+4=5xy

To find

Value of x and y

Explanation

• 6x+3y=6xy________________________(1)

• 2x+4y=5xy________________________(2)

On dividing both equations by xy

Take eq1

$= \frac{6x}{xy} + \frac{3y}{xy} = \frac{6xy}{xy}$

$= \frac{6}{y} + \frac{3y}{x} = 6$

Take eq2

$= \frac{2x}{xy} + \frac{4y}{xy} = \frac{5xy}{xy}$

$= \frac{2}{y} + \frac{4}{x} = 5$

Let 1/x=u and 1/y= v

6v+3u=6________________________(3)

2v+4u=5________________________(4)

On multiply eq 4 by 3

3(2v+4u=5)

= 6v +12u= 15__________________(5)

On subtracting eq 3 from 5

6v+12u=15

6v+3u=6

- - -

______________

9u = 9

u= 1

Putting u=1 in eq 5

6v+12u=15

6v+12×1=15

6v+12=15

6v=15-12

6v= 3

v= 3/6

v= 1/2

Before we let 1/x= u

Now,

1/x= u

1/x= 1

x=1

Before we let 1/y= v

Now,

1/y= v

1/y= 1/2

y=2

Hence,

Value of x= 1

Value of y=2

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