Maths-
General
Easy
Question
In the following system of linear equations, k is a constant and x and y are variables. For what value of k will the system of equations have no solution?
kx - 3y = 4
4x - 5y = 7
Hint:
1. An equation where no value can be substituted for the variable which will satisfy the equation i.e. for no value of x (or any other variable in the equation), would LHS equal RHS.
Hence, an equation where LHS ≠ RHS for any value of x has no solutions.
2. For Equations with No solutions:-
(a1/a2) = (b1/b2) ≠ (c1/c2)
The correct answer is: For k = 2.4, the given set of equations will have no solution
Step-by-step solution:-
From the given information, we have-
kx - 3y = 4 ….................................................. (Equation i)
4x - 5y = 7 ….................................................. (Equation ii)
Comparing the above equations with standard form of equations i.e. ax + by = c, we get-
a1 = k, b1 = -3, c1 = 4
a2 = 4, b2 = -5, c2 = 7
We know that for Equations with no solution-
(a1/a2) = (b1/b2) ≠ (c1/c2)
i.e. k/4 = -3/-5 ≠ 4/7 .................................................. (Equation iii)
∴ k/4 = -3/-5 ........................................................................... (From Equation iii)
∴ k/4 = 3/5
∴ 5k = 4 * 3 .......................................................................... (Cross multiplying)
∴ 5k = 12
∴ k = 12/5
∴ k = 2.4
Final Answer:-
∴ For k = 2.4, the given set of equations will have no solution.
Related Questions to study
Maths-
Determine whether the following equations have unique solution y = 2x + 5
y = 3x – 2.
Determine whether the following equations have unique solution y = 2x + 5
y = 3x – 2.
Maths-General
Maths-
Solve the following equation : 2(1 - x) + 5x = 3(x + 1) and say whether it is having one solution , no solution or infinitely many solutions ?
Solve the following equation : 2(1 - x) + 5x = 3(x + 1) and say whether it is having one solution , no solution or infinitely many solutions ?
Maths-General
Maths-
Given five noncollinear points, make a conjecture about the number of ways to connect different pairs of points.
Given five noncollinear points, make a conjecture about the number of ways to connect different pairs of points.
Maths-General
Maths-
Check, whether the following equation has exactly one solution or infinitely many solution or no solution. 4x + 2 = 4x – 5
Check, whether the following equation has exactly one solution or infinitely many solution or no solution. 4x + 2 = 4x – 5
Maths-General
Maths-
Write the converse and biconditional statement for the given conditional statement.
If a triangle is equilateral, then it is equiangular.
Write the converse and biconditional statement for the given conditional statement.
If a triangle is equilateral, then it is equiangular.
Maths-General
Maths-
Check, whether the following equation has exactly one solution or infinitely many solution or no solution. 4x - 5 = 2(2x - 1) – 3
Check, whether the following equation has exactly one solution or infinitely many solution or no solution. 4x - 5 = 2(2x - 1) – 3
Maths-General
Maths-
The system of equations 3x - 5y = 20 ; 6x - 10y = 40 has
The system of equations 3x - 5y = 20 ; 6x - 10y = 40 has
Maths-General
Maths-
Describe the pattern in the numbers. Write the next number in the pattern.
7, 3.5, 1.75, 0.875, …
Describe the pattern in the numbers. Write the next number in the pattern.
7, 3.5, 1.75, 0.875, …
Maths-General
Maths-
Check, whether the following equation has exactly one solution or infinitely many solution or no solution. 4x - 3 = 2x + 13
Check, whether the following equation has exactly one solution or infinitely many solution or no solution. 4x - 3 = 2x + 13
Maths-General
Maths-
Describe the pattern in the numbers. Write the next number in the pattern.
5, − 2, − 9, − 16, …
Describe the pattern in the numbers. Write the next number in the pattern.
5, − 2, − 9, − 16, …
Maths-General
Maths-
Use the Law of Detachment to make a valid conclusion in the true situation. Alex goes to the park every Sunday evening. Today is Sunday.
Use the Law of Detachment to make a valid conclusion in the true situation. Alex goes to the park every Sunday evening. Today is Sunday.
Maths-General
Maths-
For which of the values of a and b will the following pair of linear equations has infinitely many solutions x + 2y = 1; (a - b)x + (a + b)y = a + b - 2
a) a = - 3 , b = 1
b) a = 3 , b = 1
c) a = 2 , b = 2
d) None of the above
For which of the values of a and b will the following pair of linear equations has infinitely many solutions x + 2y = 1; (a - b)x + (a + b)y = a + b - 2
a) a = - 3 , b = 1
b) a = 3 , b = 1
c) a = 2 , b = 2
d) None of the above
Maths-General
Maths-
Describe the pattern in the numbers. Write the next number in the pattern.
3, 1, 1/3, 1/9, …
Describe the pattern in the numbers. Write the next number in the pattern.
3, 1, 1/3, 1/9, …
Maths-General
Maths-
In An academic contest, the Correct answer earns 12 points and the incorrect answer loses 5 points. In the final round, School A starts with 165 points and gives the same number of correct and incorrect answers. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. The game ends with the two schools tied. Find
b) How many answers did each school get correct in the final round?
In An academic contest, the Correct answer earns 12 points and the incorrect answer loses 5 points. In the final round, School A starts with 165 points and gives the same number of correct and incorrect answers. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. The game ends with the two schools tied. Find
b) How many answers did each school get correct in the final round?
Maths-General
Maths-
Classify the linear equations x = 2y and, y = 2x as having one solution, no solution or infinitely many solutions.
Classify the linear equations x = 2y and, y = 2x as having one solution, no solution or infinitely many solutions.
Maths-General
