For what value of will the equations and represent the same straight line?
Answer
k = 24
The correct answer is k = 24 — Hence k = 24.
Step-by-step solution
- Two linear equations represent the same line if one is a constant multiple of the other.
- Compare the coefficients: the second equation has coefficients exactly twice those of the first (5→10, -3→-6).
- Therefore the constant term on the right must also be twice: 2 × 12 = 24.
- Hence k = 24.
Common mistake: Forgetting to check the constant term after matching coefficients.
Concept tested: Condition for identical straight lines
Published · How this solution was prepared and checked
Related questions
- 1 For what value of k do the equations 3x + 4y = 12 and 6x + 8y = k represent the same straight line?
- 2 Determine whether the pair of equations 3x + 2y = 7 and 6x + 4y = 20 are consistent, inconsistent, or represent the same straight line. Justify your answer.
- 3 Find the values of x and y that satisfy the equations 2x + 7y = 13 and 4x - 3y = 5 using Cramer's rule.
- 4 Solve the pair of equations 4x - 7y = 2 and 3x + 5y = -1 using the elimination method.
- 5 A trader sells two types of nuts. Type A is sold at a profit of \rupee 8 per kg and Type B at a loss of \rupee 5 per kg. He sells a total of 50 kg of nuts and his overall profit is \rupee 140. How many kilograms of each type did he sell?
- 6 A small bakery makes two types of cakes. Plain cake gives a profit of \rupee 6 per cake and chocolate cake gives a loss of \rupee 4 per cake. If the bakery sells a total of 40 cakes in a day and the net profit is \rupee 80, how many plain and how many chocolate cakes were sold?