Advertisements
Advertisements
प्रश्न
Solve for x and y :
`[ y + 7 ]/5 = [ 2y - x ]/4 + 3x - 5`
`[ 7 - 5x ]/2 + [ 3 - 4y ]/6 = 5y - 18`
उत्तर
The given pair of linear equation are
`[ y + 7 ]/5 = [ 2y - x ]/4 + 3x - 5`
⇒ 55x + 6y = 128 ....(1)[ On simplifying ]
`[ 7 - 5x ]/2 + [ 3 - 4y ]/6 = 5y - 18`
⇒ 15x + 34y = 132 ....(2)[ On simplifying ]
Multiply equation (1) by 3 and equation (2) by 11, we get :
165x + 18y = 384 ....(3)
165x + 374y = 1452 .....(4)
Subtracting (4) from (3)
165x + 18y = 384
- 165x + 374y = 1452
- - -
- 356y = - 1068
y = 3
Substituting y = 3 in equation (1), we get
55x + 6(3) = 128
⇒ 55x = 110
⇒ x = 2
∴ Solution is x = 2 and y = 3.
APPEARS IN
संबंधित प्रश्न
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 )
For solving pair of equation, in this exercise use the method of elimination by equating coefficients :
2x - 3y - 3 = 0
`[2x]/3 + 4y + 1/2` = 0
If 2x + y = 23 and 4x - y = 19; find the values of x - 3y and 5y - 2x.
Solve the following simultaneous equations :
6x + 3y = 7xy
3x + 9y = 11xy
Solve the following pairs of equations:
`x/(3) + y/(4)` = 11
`(5x)/(6) - y/(3)` = -7
If the following three equations hold simultaneously for x and y, find the value of 'm'.
2x + 3y + 6 = 0
4x - 3y - 8 = 0
x + my - 1 = 0
Anil and Sunita have incomes in the ratio 3 : 5. If they spend in the ratio 1 : 3, each saves T 5000. Find the income of each.
A person goes 8 km downstream in 40 minutes and returns in 1 hour. Determine the speed of the person in still water and the speed of the stream.
Salman and Kirti start at the same time from two places 28 km apart. If they walk in the same direction, Salman overtakes Kirti in 28 hours but if they walk in the opposite directions, they meet in 4 hours. Find their speeds (in km/h).
Two mobiles S1 and S2 are sold for Rs. 10,490 making 4% profit on S1 and 6% on S2. If the two mobiles are sold for Rs.10,510, a profit of 6% is made on S1 and 4% on S2. Find the cost price of both the mobiles.
