Advertisements
Advertisements
प्रश्न
Solve the following pairs of equations by reducing them to a pair of linear equations
`1/(2x) + 1/(3y) = 2`
`1/(3x) + 1/(2y) = 13/6`
उत्तर
`1/(2x) + 1/(3y) = 2`
`1/(3x) + 1/(2y) = 13/6`
Let `1/x = p ` , then the equations changes as below:
`p/2 + q/3 = 2 ` ⇒ 3p + 2q -12 = 0 ... (i)
`p/3 + q/2 = 13/6` ⇒ 2p + 3q -13 = 0 ... (ii)
By cross-multiplication method, we get
`p/(-26-(-36)) = q/(-24-(-39)) = 1/(9-4)`
`p/10 = q/15 = 1/5`
`p/10 = 1/5 `
p = 2 and q = 3
1/x = 2 and 1/y = 3
Hence, `x = 1/2 `
APPEARS IN
संबंधित प्रश्न
Solve the following system of equations `\frac { 1 }{ 2x } – \frac { 1 }{ y } = – 1; \frac { 1 }{ x } + \frac { 1}{ 2y } = 8`
Solve `\frac { 2 }{ x } + \frac { 1 }{ 3y } = \frac { 1}{ 5 }; \frac { 3 }{ x } + \frac { 2 }{ 3y } = 2` and also find ‘a’ for which y = ax – 2
Solve the following pairs of equations by reducing them to a pair of linear equations
`1/(3x+y) + 1/(3x-y) = 3/4`
`1/(2(3x-y)) - 1/(2(3x-y)) = (-1)/8`
The ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differ by 30 years. Find the ages of Ani and Biju
Find the values of following determinant.
`|(7/3,5/3), (3/2, 1/2)|`
A two-digit number is such that the product of its digits is 20. If 9 is added to the number, the digits interchange their places. Find the number.
Let the numerator and denominator of the fraction be x and y respectively. Then the fraction is `x/y`
If the numerator is multiplied by 2 and the denominator is reduced by 5, the fraction becomes `6/5`. Thus, we have
`(2x)/(y-5)=6/5`
`⇒ 10x=6(y-5)`
`⇒ 10x=6y-30`
`⇒ 10x-6y+30 =0`
`⇒ 2(5x-3y+15)=0`
`⇒ 5x - 3y+15=0`
If the denominator is doubled and the numerator is increased by 8, the fraction becomes `2/5`. Thus, we have
`(x+8)/(2y)=2/5`
`⇒ 5(x+8)=4y`
`⇒ 5x+40=4y`
`⇒ 5x-4y+40=0`
So, we have two equations
`5x-3y+15=0`
`5x-4y+40=0`
Here x and y are unknowns. We have to solve the above equations for x and y.
By using cross-multiplication, we have
`x/((-3)xx40-(-4)xx15)=-y/(5xx40-5xx15)=1/(5xx(-4)-5xx(-3))`
`⇒ x/(-120+60)=(-y)/(200-75)=1/(-20+15)`
`⇒x/(-60)=-y/125``=1/-5`
`⇒ x= 60/5,y=125/5`
`⇒ x=12,y=25`
Hence, the fraction is `12/25`
The sum of the numerator and denominator of a fraction is 4 more than twice the numerator. If the numerator and denominator are increased by 3, they are in the ratio 2 : 3. Determine the fraction.
The sum of the numerator and denominator of a fraction is 3 less than twice the denominator. If the numerator and denominator are decreased by 1, the numerator becomes half the denominator. Determine the fraction.
State with reason whether the point (3, −2) will lie on the graph of the equation 5m – 3n = − 21
