Class 10 Exam > Class 10 Questions > If 6x + 3y= 6xy ; 2x + 4y = 5xy, then the val...
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If 6x + 3y= 6xy ; 2x + 4y = 5xy, then the values of xand y are
- a)½ and 1
- b)1 and 2
- c)2 and 1
- d)1 and ½
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If 6x + 3y= 6xy ; 2x + 4y = 5xy, then the values of xand y area)Â...
The first equation is 6x + 3y = 6xy, which can be rewritten as 6x - 6xy = -3y.
Factoring out x from the left side gives: x(6 - 6y) = -3y.
Dividing both sides by (6 - 6y) gives: x = (-3y) / (6 - 6y).
The second equation is 2x + 4y = 5xy, which can be rewritten as 2x - 5xy = -4y.
Factoring out x from the left side gives: x(2 - 5y) = -4y.
Dividing both sides by (2 - 5y) gives: x = (-4y) / (2 - 5y).
Since both equations are equal to x, we can set the right sides equal to each other:
(-3y) / (6 - 6y) = (-4y) / (2 - 5y).
Cross multiplying gives: (-3y)(2 - 5y) = (-4y)(6 - 6y).
Expanding gives: -6y + 15y^2 = -24y + 24y^2.
Combining like terms gives: 15y^2 - 6y = 24y^2 - 24y.
Subtracting (15y^2 - 6y) from both sides gives: 0 = 9y^2 - 18y.
Factoring out y gives: 0 = y(9y - 18).
Setting each factor equal to zero gives: y = 0 or 9y - 18 = 0.
Solving the second equation for y gives: 9y = 18, y = 2.
Substituting y = 2 into the first equation gives: 6x + 3(2) = 6x(2), 6x + 6 = 12x.
Subtracting 6x from both sides gives: 6 = 6x.
Dividing both sides by 6 gives: x = 1.
Therefore, the values of x and y are x = 1 and y = 2.
Answer: a) x = 1 and y = 2.
Factoring out x from the left side gives: x(6 - 6y) = -3y.
Dividing both sides by (6 - 6y) gives: x = (-3y) / (6 - 6y).
The second equation is 2x + 4y = 5xy, which can be rewritten as 2x - 5xy = -4y.
Factoring out x from the left side gives: x(2 - 5y) = -4y.
Dividing both sides by (2 - 5y) gives: x = (-4y) / (2 - 5y).
Since both equations are equal to x, we can set the right sides equal to each other:
(-3y) / (6 - 6y) = (-4y) / (2 - 5y).
Cross multiplying gives: (-3y)(2 - 5y) = (-4y)(6 - 6y).
Expanding gives: -6y + 15y^2 = -24y + 24y^2.
Combining like terms gives: 15y^2 - 6y = 24y^2 - 24y.
Subtracting (15y^2 - 6y) from both sides gives: 0 = 9y^2 - 18y.
Factoring out y gives: 0 = y(9y - 18).
Setting each factor equal to zero gives: y = 0 or 9y - 18 = 0.
Solving the second equation for y gives: 9y = 18, y = 2.
Substituting y = 2 into the first equation gives: 6x + 3(2) = 6x(2), 6x + 6 = 12x.
Subtracting 6x from both sides gives: 6 = 6x.
Dividing both sides by 6 gives: x = 1.
Therefore, the values of x and y are x = 1 and y = 2.
Answer: a) x = 1 and y = 2.
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Community Answer
If 6x + 3y= 6xy ; 2x + 4y = 5xy, then the values of xand y area)Â...
• 6x + 3y = 6xy..(i)
• 2x + 4y = 5xy..(ii)
{ for ( iii ) equation , multiply ( ii ) equation by 3 }
• 6x + 12y = 15xy..(iii)
|| Subtract (i) from (iii) equation ||
( 6x + 12 y = 15xy ) - ( 6x + 3y = 6xy )
= 9y = 9xy
= 9y = 9y ( x ) { x = 9y/9y }
= x = 1
Putting the value of x in 1st , we get the value of " y " ,i.e.,
6 × 1 + 3y = 6 × 1 × y
6 + 3y = 6y
6 = 6y - 3y
6 = 3y
y = 2
Therefore we get the value , x = 1 & y = 2 ; Hence , Option B is correct .
• 2x + 4y = 5xy..(ii)
{ for ( iii ) equation , multiply ( ii ) equation by 3 }
• 6x + 12y = 15xy..(iii)
|| Subtract (i) from (iii) equation ||
( 6x + 12 y = 15xy ) - ( 6x + 3y = 6xy )
= 9y = 9xy
= 9y = 9y ( x ) { x = 9y/9y }
= x = 1
Putting the value of x in 1st , we get the value of " y " ,i.e.,
6 × 1 + 3y = 6 × 1 × y
6 + 3y = 6y
6 = 6y - 3y
6 = 3y
y = 2
Therefore we get the value , x = 1 & y = 2 ; Hence , Option B is correct .
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If 6x + 3y= 6xy ; 2x + 4y = 5xy, then the values of xand y area)½ and 1b)1 and 2c)2 and 1d)1 and ½Correct answer is option 'B'. Can you explain this answer?
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