Advertisements
Advertisements
प्रश्न
Solve the following pairs of equations:
`(3)/x - (1)/y` = -9
`(2)/x + (3)/y` = 5
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 :
`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 :
3 - (x - 5) = y + 2
2 (x + y) = 4 - 3y
For solving pair of equation, in this exercise use the method of elimination by equating coefficients :
41x + 53y = 135
53x + 41y = 147
Solve the following simultaneous equations:
13a - 11b = 70
11a - 13b = 74
Solve the following pairs of equations:
`(xy)/(x + y) = (6)/(5)`
`(xy)/(y - x)` = 6
Where x + y ≠ 0 and y - x ≠ 0
If 2x + y = 23 and 4x - y = 19 : find the value of x - 3y and 5y - 2x.
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.
In a triangle, the sum of two angles is equal to the third angle. If the difference between these two angles is 20°, determine all the angles.
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.
Two mobiles S1 and S2 are sold for Rs. 10,490 making 4% profit on S1 and 6% on S2. If the two mobiles are sold for Rs.10,510, a profit of 6% is made on S1 and 4% on S2. Find the cost price of both the mobiles.
