List of top Mathematics Questions on Linear Equations

The sum of two numbers is 50 and one number is \(\frac{7}{3}\) times of the other; then find the numbers.
If the system of equations $ 2x + 3y - 3z = 3,\ x + 2y + \alpha z = 1,\ 2x - y + z = \beta $ has infinitely many solutions, then $ \frac{\alpha}{\beta} = \frac{\beta}{\alpha} $
A pair of linear equations \( a_1 x + b_1 y + c_1 = 0 \) and \( a_2 x + b_2 y + c_2 = 0 \) is such that \( \frac{a_1}{a_2} \neq \frac{b_1}{b_2} \), then they are:
If \( x - 4y - 14 = 0 \) and \( 5x - y - 13 = 0 \) will have:
The lines \( 2x + 3y - 9 = 0 \) and \( 4x + 6y - 18 = 0 \) are:
If \( 5f(x) + 4f\left(\frac{1}{x}\right) = x^2 - 2 \), for all \( x \neq 0 \), and \( y = 9x^2f(x) \), then \( y \) is strictly increasing in:
Reena is twice as old as Sunitha. Three years ago, she was three times as old as Sunitha. How old is Reena now?
Sum of two numbers is 21 and their difference is 11, then the greatest number is
If \(x + y = 7\) and \(3x - 2y = 11\), then
If \(2x + y = 35\) and \(3x + 4y = 65\), then the value of \(\frac{x}{y}\) is
Two supplementary angles measure \(5x + 15^\circ\) and \(4x - 6^\circ\), angle are
Consider the system of linear equations
x + y + z = 5,
x + 2y + λ2z = 9,
x + 3y + λz = μ,
where λ, μ ∈ ℝ.Then, which of the following statement is NOT correct?
The sum of two numbers is 18, and the sum of their reciprocals is $\frac{1}{4}$. Find the numbers.
The sum of two numbers is 18, and the sum of their reciprocals is $\frac{1}{4}$. Find the numbers.
A linear programming problem deals with the optimization of a/an:
If cost of 4 chairs and 7 tables is Rs. 360 and cost of 6 chairs and 10 tables is Rs. 520, then find the cost of one chair and one table separately.
The sum of the digits of a two-digit number is 9. If the digits of the number be interchanged then the new number is 27 more than the original number. Find the number.
In the system of equations $\dfrac{x}{a} = \dfrac{y}{b}$, $ax + by = a^2 + b^2$, value of y will be
If the difference of two numbers is 26 and one number be three times the other, then find the numbers.
The sum of a two-digit number and the number obtained by reversing the order of its digits is 66. If the digits differ by 2, find the number.
The value of \(p\), for which the pair of equations \(3x + 4y + 2 = 0\) and \(9x + py + 8 = 0\) represents parallel lines, is:
If \(\frac{2}{\sqrt{x}} = 2\) and \(\frac{4}{\sqrt{y}} = -1\), then
The pair of equations \(x + y = 5\) and \(2x + 2y = k\) has infinitely many solutions if \(k =\)
Nimra went to a bank to withdraw ₹2,000. She asked the cashier to give her ₹50 and ₹100 notes only and she got 30 notes in all. How many notes of ₹50 and ₹100 respectively that she received?
Which of the following equation represents the situation where Kiran bought 5 oranges, 7 apples, and Harish bought 2 oranges, 12 apples for the same amount of total money?