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 :
13 + 2y = 9x
3y = 7x
For solving pair of equation, in this exercise use the method of elimination by equating coefficients :
13x+ 11y = 70
11x + 13y = 74
Solve for x and y :
`[ y + 7 ]/5 = [ 2y - x ]/4 + 3x - 5`
`[ 7 - 5x ]/2 + [ 3 - 4y ]/6 = 5y - 18`
Find the value of m, if x = 2, y = 1 is a solution of the equation 2x + 3y = m.
The value of expression mx - ny is 3 when x = 5 and y = 6. And its value is 8 when x = 6 and y = 5. Find the values of m and n.
Solve :
`4x + [ x - y ]/8 = 17`
`2y + x - [ 5y + 2 ]/3 = 2`
Solve the following pairs of equations:
`(3)/(5) x - (2)/(3) y + 1` = 0
`(1)/(3) y + (2)/(5) x ` = 4
Solve the following pairs of equations:
`(5)/(x + y) - (2)/(x - y)` = -1
`(15)/(x + y) + (7)/(x - y)` = 10.
`(3)/x - (2)/y` = 0 and `(2)/x + (5)/y` = 19, Hence, find a if y = ax + 3.
A solution containing 12% alcohol is to be mixed with a solution containing 4% alcohol to make 20 gallons of solution containing 9% alcohol. How much of each solution should be used?
