Advertisements
Advertisements
Question
Solve :
`[ 7 + x ]/5 - [ 2x - y ]/4 = 3y - 5`
`[5y - 7]/2 + [ 4x - 3 ]/6 = 18 - 5x`
Advertisements
Solution
`[ 7 + x ]/5 - [ 2x - y ]/4 = 3y - 5` .....(Given)
⇒ 4( 7 + x ) - 5( 2x - y ) = 20( 3y - 5 )
⇒ 28 + 4x - 10x + 5y = 60y - 100
⇒ - 6x - 55y = - 128 ......(1)
`[5y - 7]/2 + [ 4x - 3 ]/6 = 18 - 5x` ......(Given)
⇒ 3(5y - 7) + 4x - 3 = 6( 18 - 5x )
⇒ 15y - 21 + 4x - 3 = 108 - 30x
⇒ 34x + 15y = 132 .......(2)
Multiplying equation (1) by 34 and equation (2) by 6, We get
- 204x - 1870y = - 4352 .....(3)
204x + 90y = 792 ......(4)
Adding equation (3) and (4), We get
- 204x - 1870y = - 4352 .....(3)
+ 204x + 90y = 792
- 1780y = -3560
⇒ y = 2
Substituting y = 2 in equation (1), We get
- 6x - 55 x 2 = - 128
⇒ - 6x - 110 = - 128
⇒ - 6x = - 18
⇒ x = 3
∴ Solution is x = 3 and y = 2.
APPEARS IN
RELATED QUESTIONS
For solving pair of equation, in this exercise use the method of elimination by equating coefficients :
`[ x - y ]/6 = 2( 4 - x )`
2x + y = 3( x - 4 )
If 10y = 7x - 4 and 12x + 18y = 1; find the values of 4x + 6y and 8y - x.
Solve for x and y :
`[ y + 7 ]/5 = [ 2y - x ]/4 + 3x - 5`
`[ 7 - 5x ]/2 + [ 3 - 4y ]/6 = 5y - 18`
Solve :
11(x - 5) + 10(y - 2) + 54 = 0
7(2x - 1) + 9(3y - 1) = 25
Solve the following simultaneous equations :
6x + 3y = 7xy
3x + 9y = 11xy
Solve the following simultaneous equations:
13a - 11b = 70
11a - 13b = 74
Solve the following pairs of equations:
`(2)/(3x + 2y) + (3)/(3x - 2y) = (17)/(5)`
`(5)/(3x + 2y) + (1)/(3x - 2y)` = 2
The length of a rectangle is twice its width. If its perimeter is 30 units, find its dimensions.
In a two-digit number, the sum of the digits is 7. The difference of the number obtained by reversing the digits and the number itself is 9. Find the number.
The present ages of Kapil and Karuna are in the ratio 2 : 3. Six years later, the ratio will be 5 : 7. Find their present ages.
