Advertisements
Advertisements
प्रश्न
Solve the following pairs of equations:
`(3)/x - (1)/y` = -9
`(2)/x + (3)/y` = 5
Advertisements
उत्तर
The given equations are `(3)/x - (1)/y` = -9 and `(2)/x + (3)/y` = 5
Let `(1)/x = "a" and (1)/y = "b"`
Then, we have
3a - b = -9 ....(i)
2a + 3b = 5 ....(ii)
Multiplying eqn. (i) by 3, we get
9a - 3b = -27 ....(iii)
Adding eqns. (ii) and (iii), we get
11a = -22
⇒ a = -2
⇒`(1)/x` = -2
⇒ x = `-(1)/(2)`
Substituting the value of a in eqn. (i), we get
3(-2) -b = -9
⇒ -6 - b = -9
⇒ b = -6 + 9
⇒ b = 3
⇒ `(1)/y` = 3
⇒ y = `(1)/(3)`
Thus, the solution set is `(-1/2, 1/3)`.
APPEARS IN
संबंधित प्रश्न
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 :
`[ x - y ]/6 = 2( 4 - x )`
2x + y = 3( x - 4 )
Solve for x and y:
4x = 17 - `[ x - y ]/8`
2y + x = 2 + `[ 5y + 2 ]/3`
Solve the following simultaneous equation :
8v - 3u = 5uv
6v - 5u = -2uv
`4x + 6/y = 15 and 6x - 8/y = 14.` Hence, find a if y = ax - 2.
The sum of a two-digit number and the number obtained by reversing the digits is 110 and the difference of two digits is 2. Find the number.
The present ages of Kapil and Karuna are in the ratio 2 : 3. Six years later, the ratio will be 5 : 7. Find their present ages.
An eraser costs Rs. 1.50 less than a sharpener. Also, the cost of 4 erasers and 3 sharpeners is Rs.29. Taking x and y as the costs (in Rs.) of an eraser and a sharpener respectively, write two equations for the above statements and find the value of x and y.
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.
A and B can build a wall in `6(2)/(3)` days. If A's one day work is `1(1)/(4)` of one day work of B, find in 4 how many days A and B alone can build the wall.
