Advertisements
Advertisements
Question
Find the value of k for which the system of equations x + 2y – 3 = 0 and 5x + ky + 7 = 0 is inconsistent.
Solution
The given system is
x + 2y – 3 = 0 ……(i)
5x + ky + 7 = 0 ……(ii)
Here, `"a"_1 = 1, "b"_1 = 2, "c"_1 = -3, "a"_2 = 5, "b"_2 = "k" and "c"_2 = 7.`
For the system, to be inconsistent, we must have
`("a"_1)/("a"_2) =("b"_1)/("b"_2) ≠ ("c"_1)/("c"_2)`
`⇒ 1/5 = 2/"k" ≠ (−3)/7`
`⇒ 1/5 = 2/"k"`
⇒ k = 10
Hence, k = 10
APPEARS IN
RELATED QUESTIONS
Speed of a boat in still water is 15 km/h. It goes 30 km upstream and returns back at the same point in 4 hours 30 minutes. Find the speed of the stream.
Find the value of k for which each of the following system of equations has infinitely many solutions :
\[kx + 3y = 2k + 1\]
\[2\left( k + 1 \right)x + 9y = 7k + 1\]
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:
2x + 3y = 7
(a - 1)x + (a + 1)y = (3a - 1)
A railway half ticket costs half the full fare and the reservation charge is the some on half ticket as on full ticket. One reserved first class ticket from Mumbai to Delhi costs ₹4150 while one full and one half reserved first class ticket cost ₹ 6255. What is the basic first class full fare and what is the reservation charge?
If twice the son’s age in years is added to the mother’s age, the sum is 70 years. But, if twice the mother’s age is added to the son’s age, the sum is 95 years. Find the age of the mother and that of the son.
In a cyclic quadrilateral ABCD, it is given ∠A = (2x + 4)°, ∠B = (y + 3)°, ∠C = (2y + 10)° and ∠D = (4x – 5)°. Find the four angles.
Find the value of k, if the point P (2, 4) is equidistant from the points A(5, k) and B (k, 7).
a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, where a1, b1, c1, a2, b2, c2 are all real numbers and a12+ b12 ≠ 0, a22 + b22 ≠ 0, is called a ______.
If x = a, y = b is the solution of the equations x – y = 2 and x + y = 4, then the values of a and b are, respectively ______.
