Advertisements
Advertisements
Question
If 10y = 7x - 4 and 12x + 18y = 1 ; find the value of 4x + 6y and 8y - x.
Advertisements
Solution
10y = 7x - 4 ........(1)
12x + 18y = 1 ........(2)
Multiplying (1) by 9 and (2) by 5, we get,
63x - 90y = 36 ........(3)
60x + 90y = 5 ........(4)
Adding (3) and (4), we get,
123x = 41
⇒ x = `(41)/(123) = (1)/(3)`
∴ 10y = `(7)/(3) - 4`
= `(7 - 12)/(3)`
= `(-5)/(3)`
⇒ y = `(-5)/(3) xx (1)/(10)`
= `(-1)/(6)`
∴ 4x + 6y = `(4)/(3) - 1`
= `(1)/(3)`
8y - x
= `(-8)/(6) - (1)/(3)`
= `(-8 - 2)/(6)`
= `(-10)/(6)`
= `(-5)/(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
For solving pair of equation, in this exercise use the method of elimination by equating coefficients:
y = 2x - 6; y = 0
For solving pair of equation, in this exercise use the method of elimination by equating coefficients :
41x + 53y = 135
53x + 41y = 147
Solve :
`4x + [ x - y ]/8 = 17`
`2y + x - [ 5y + 2 ]/3 = 2`
Solve the following simultaneous equations :
6x + 3y = 7xy
3x + 9y = 11xy
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:
y - x = 0.8
`(13)/(2(x + y)) = 1`
Solve the following pairs of equations:
`(2)/(3x + 2y) + (3)/(3x - 2y) = (17)/(5)`
`(5)/(3x + 2y) + (1)/(3x - 2y)` = 2
The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes `(1)/(2)`. Find the fraction.
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.
