Advertisements
Advertisements
Question
`(3)/x - (2)/y` = 0 and `(2)/x + (5)/y` = 19, Hence, find a if y = ax + 3.
Advertisements
Solution
`(3)/x - (2)/y` = 0 __________(1)
`(2)/x + (5)/y` = 19 _________(2)
Multiplying (1) by 5 and (2) by 2, we get,
`(15)/x - (10)/y` = 0 _________(3)
`(4)/x + (10)/y` = 38 _________(4)
Adding (3) and (4), we get,
`(19)/x` = 38
⇒ x = `(19)/(38)`
= `(1)/(2)`
Now, `(3)/x = (2)/y`
⇒ `(2)/y` = 6
⇒ y = `(2)/(6)`
= `(1)/(3)`
Thus, the solution set is `(1/2, 1/3)`.
Now, y = ax + 3
⇒ `(1)/(3)`
= `(1)/(2)"a" + 3`
⇒ `"a"/(2)`
= `(1)/(3) - 3`
= `(1 - 9)/(3)`
= `(-8)/(3)`
⇒ a = `(-8)/(3) xx 2`
= `(-16)/(3)`
= `-5(1)/(3)`.
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
Find the value of m, if x = 2, y = 1 is a solution of the equation 2x + 3y = m.
10% of x + 20% of y = 24
3x - y = 20
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 :
11(x - 5) + 10(y - 2) + 54 = 0
7(2x - 1) + 9(3y - 1) = 25
Solve the following pairs of equations:
`(2)/x + (3)/y = (9)/(xy)`
`(4)/x + (9)/y = (21)/(xy)`
Where x ≠ 0, y ≠ 0
Solve the following pairs of equations:
`(2)/(x + 1) - (1)/(y - 1) = (1)/(2)`
`(1)/(x + 1) + (2)/(y - 1) = (5)/(2)`
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
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?
