Advertisements
Advertisements
प्रश्न
Solve for x and y:
`a^2x + b^2y = c^2, b^2x + a^2y = d^2`
उत्तर
The given equations are
`a^2x + b^2y = c^2` ………(i)
`b^2x + a^2y = d^2` ………(ii)
Multiplying (i) by `a^2 and (ii) by b^2` and subtracting, we get
`a^4x – b^4x = a^2c^2 - b^2 d^2`
`⇒x = (a^2c^2−b^2d^2)/ (a^4− b^4)`
Now, multiplying (i) by `b^2` and (ii) by `a^2` and subtracting, we get
`b^4y – a^4y = b^2c2 - a^2 d^2`
`⇒y =(b^2 c^2−a^2d^2)/ (b^4− a^4)`
Hence,` x = (a^2c^2−b^2d^2)/( a^4− b^4) and y = (b^2c^2−a^2d^2)/(b^4− a^4)`.
APPEARS IN
संबंधित प्रश्न
Draw the graph of
(i) x – 7y = – 42
(ii) x – 3y = 6
(iii) x – y + 1 = 0
(iv) 3x + 2y = 12
Find the value of k for which each of the following system of equations have infinitely many solutions:
2x − 3y = 7
(k + 2)x − (2k + 1)y − 3(2k − 1)
Obtain the condition for the following system of linear equations to have a unique solution
ax + by = c
lx + my = n
Find the values of a and b for which the following system of equations has infinitely many solutions:
(2a - 1)x - 3y = 5
3x + (b - 2)y = 3
Solve for x and y:
0.3x + 0.5y = 0.5, 0.5x + 0.7y = 0.74
A lady has only 50-paisa coins and 25-paisa coins in her purse. If she has 50 coins in all totaling Rs.19.50, how many coins of each kind does she have?
A two-digit number is 3 more than 4 times the sum of its digits. If 18 is added to the number, the digits are reversed. Find the number.
A part of monthly hostel charges in a college are fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 25days, he has to pay Rs. 4550 as hostel charges whereas a student B, who takes food for 30 days, pays Rs. 5200 as hostel charges. Find the fixed charges and the cost of the food per day.
Show that the system 2x + 3y -1= 0 and 4x + 6y - 4 = 0 has no solution.
Solve for x:
