Advertisements
Advertisements
Question
Solve for x and y :
`[ y + 7 ]/5 = [ 2y - x ]/4 + 3x - 5`
`[ 7 - 5x ]/2 + [ 3 - 4y ]/6 = 5y - 18`
Advertisements
Solution
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
RELATED QUESTIONS
For solving pair of equation, in this exercise use the method of elimination by equating coefficients :
`1/5( x - 2 ) = 1/4( 1 - y )`
26x + 3y + 4 = 0
Solve for x and y:
4x = 17 - `[ x - y ]/8`
2y + x = 2 + `[ 5y + 2 ]/3`
Solve :
11(x - 5) + 10(y - 2) + 54 = 0
7(2x - 1) + 9(3y - 1) = 25
Solve the following pairs of equations:
y - x = 0.8
`(13)/(2(x + y)) = 1`
Solve the following pairs of equations:
`(2)/(x + 1) - (1)/(y - 1) = (1)/(2)`
`(1)/(x + 1) + (2)/(y - 1) = (5)/(2)`
Can the following equations hold simultaneously?
7y - 3x = 7
5y - 11x = 87
5x + 4y = 43
If yes, find the value of x and y.
The length of a rectangle is twice its width. If its perimeter is 30 units, find its dimensions.
A boat goes 18 km upstream in 3 hours and 24 km downstream in 2 hours. Find the speed of the boat 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).
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?
