Advertisements
Advertisements
Question
Find the value of k for which each of the following system of equations have no solution :
2x + ky = 11
5x − 7y = 5
Solution
The given system of equation is
2x + ky - 11 =0
5x − 7y - 5 = 0
The system of equation is of the form
`a_1x + b_1y + c_1 = 0`
`a_2x + b_2y + c_2 = 0`
Where, `a_1 = 2,b_1 = k, c_1 = -11`
And `a_2 = 5, b_2 = -7, c_2 = -5`
For a unique solution, we must have
`a_1/a_2 - b_1/b_2 != c_1/c_2`
`=> 2/5 = k/(-7) != (-11)/(-5)`
Now
`2/5 = k/(-7)`
`=> 2 xx (-7) = 5k`
`=> 5k = -14`
`=> k = (-14)/5`
Cleary for `(-14)/5` we have `k/(-7) != (-11)/(-5)`
Hence, the given system of equation will have no solution if `k = (-14)/5`
APPEARS IN
RELATED QUESTIONS
The cost of 2 kg of apples and 1 kg of grapes on a day was found to be Rs 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs 300. Represent the situation algebraically and geometrically.
Find the value of k for which each of the following systems of equations has infinitely many solutions :
4x + 5y = 3
kx + 15y = 9
Solve for x and y:
`10/(x+y) + 2/(x−y) = 4, 15/(x+y) - 9/(x−y) = -2, where x ≠ y, x ≠ -y.`
Solve for x and y:
`1/(3x+y) + 1/(3x−y) = 3/4, 1/(2(3x+y)) - 1/(2(3x−y)) = −1/8`
Solve for x and y:
`x + y = a + b, a x – by = a^2 – b^2`
Show that the following system of equations has a unique solution:
3x + 5y = 12,
5x + 3y = 4.
Also, find the solution of the given system of equations.
The difference of two numbers is 5 and the difference between their squares is 65. Find the numbers.
If 12x + 17y = 53 and 17x + 12y = 63 then find the value of ( x + y)
Read the following passage:
 Lokesh, a production manager in Mumbai, hires a taxi everyday to go to his office. The taxi charges in Mumbai consists of a fixed charges together with the charges for the distance covered. His office is at a distance of 10 km from his home. For a distance of 10 km to his office, Lokesh paid ₹ 105. While coming back home, he took another roµte. He covered a distance of 15 km and the charges paid by him were ₹ 155. |
Based on the above information, answer the following questions:
- What are the fixed charges?
- What are the charges per km?
- If fixed charges are ₹ 20 and charges per km are ₹ 10, then how much Lokesh have to pay for travelling a distance of 10 km?
OR
Find the total amount paid by Lokesh for travelling 10 km from home to office and 25 km from office to home. [Fixed charges and charges per km are as in (i) and (ii).
If 17x + 15y = 11 and 15x + 17y = 21, then find the value of x − y.
