Advertisements
Advertisements
प्रश्न
Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method.
x – 3y – 7 = 0
3x – 3y – 15 = 0
उत्तर
x – 3y – 7 = 0
3x – 3y – 15= 0
`a_1/a_2 = 1/3`
`b_1/b_2 = (-3)/-3 = 1 `
`c_1/c_2 = (-7)/-15 = 7/15`
`a_1/a_2 ≠ b_1/b_2`
Therefore, they will intersect each other at a unique point and thus, there will be a unique solution for these equations.
By cross-multiplication,
`x/(45-(21)) = y/(-21-(-15)) = 1/(-3-(-9))`
`x/24 = y/-6 = 1/6`
x/24 = 1/6 and y/-6 = 1/6
x = 4 and y = -1
∴ x = 4, y = -1.
APPEARS IN
संबंधित प्रश्न
A thief runs with a uniform speed of 100 m/minute. After one minute, a policeman runs after the thief to catch him. He goes with a speed of 100 m/minute in the first minute and increases his speed by 10 m/minute every succeeding minute. After how many minutes the policeman will catch the thief.
Solve the follownig system of equations by the method of cross-multiplication.
2x – 6y + 10 = 0
3x – 7y + 13 = 0
Solve the following system of equations by the method of cross-multiplication.
11x + 15y = – 23; 7x – 2y = 20
Solve the following system of equations by cross-multiplication method x + y = a – b; ax – by = a2 + b2
Solve each of the following systems of equations by the method of cross-multiplication :
`x(a - b + (ab)/(a - b)) = y(a + b - (ab)/(a + b))`
`x + y = 2a^2`
Solve the system of equation by using the method of cross multiplication:
`5/("x+y") - 2/("x− y") + 1 = 0, 15/("x+y") + 7/("x− y") – 10 = 0`
Solve 0.4x + 0.3y = 1.7; 0.7 x − 0.2y = 0.8
Ankita travels 14 km to her home partly by rickshaw and partly by bus. She takes half an hour if she travels 2 km by rickshaw, and the remaining distance by bus. On the other hand, if she travels 4 km by rickshaw and the remaining distance by bus, she takes 9 minutes longer. Find the speed of the rickshaw and of the bus.
A two-digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting 5 or by multiplying the difference of the digits by 16 and then adding 3. Find the number.
A railway half ticket costs half the full fare, but the reservation charges are the same on a half ticket as on a full ticket. One reserved first class ticket from the station A to B costs Rs 2530. Also, one reserved first class ticket and one reserved first class half ticket from A to B costs Rs 3810. Find the full first class fare from station A to B, and also the reservation charges for a ticket.
