Advertisements
Advertisements
Question
Solve the following pairs of equations:
`(3)/(5) x - (2)/(3) y + 1` = 0
`(1)/(3) y + (2)/(5) x ` = 4
Advertisements
Solution
`(3)/(5) x - (2)/(3) y + 1` = 0
⇒ 9x - 10y + 15 = 0
⇒ 9x - 10y = -15 ....(i)
`(1)/(3)y + (2)/(5)x` = 4
⇒ 5y + 6x = 60
⇒ 6x + 5y = 60 ....(ii)
Multiplying eqn. (ii) by 2, we get
12x + 10y = 120 ....(iii)
Adding eqns. (i) and (iii), we get
21x = 105
⇒ x = 5
Substituting the value of x in eqn. (ii), we get
6(5) + 5y = 60
⇒ 30 + 5y = 60
⇒ 5y = 30
⇒ y = 6
Thus, the solution set is (5,6).
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:
y = 2x - 6; y = 0
Find the value of m, if x = 2, y = 1 is a solution of the equation 2x + 3y = m.
Solve the following simultaneous equations:
65x - 33y = 97
33x - 65y = 1
Solve the following pairs of equations:
`(2)/(3x + 2y) + (3)/(3x - 2y) = (17)/(5)`
`(5)/(3x + 2y) + (1)/(3x - 2y)` = 2
If 10y = 7x - 4 and 12x + 18y = 1 ; find the value of 4x + 6y and 8y - x.
In a two-digit number, the sum of the digits is 7. The difference of the number obtained by reversing the digits and the number itself is 9. Find the number.
The ratio of two numbers is `(2)/(5)`. If 4 is added in first and 32 is subtracted from the second, the ratio becomes the reciprocal of the original ratio. Find the numbers.
If 1 is added to the denominator of a fraction, the fraction becomes `(1)/(2)`. If 1 is added to the numerator of the fraction, the fraction becomes 1. Find the fraction.
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.
