List of top Mathematics Questions on Linear Equations asked in UP Board X

The sum of a two-digit number and the number obtained by reversing the digits is 110. If the tens digit of the number is 6 more than the units digit, then find the number.

Solve the following pairs of linear equations : $3x - 5y = 4$, $9x = 2y + 7$
In linear equation $\frac{x}{3} + \frac{y}{2} = 6$ if $x = 9$ then the value of $y$ will be :
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.
Solve the following pair of equations: \[ \frac{3}{x} + \frac{2}{y} = 11, \quad \frac{4}{x} - \frac{5}{y} = 7. \]
Find the value of \( k \) for which the equations \( 2x + ky = 1 \) and \( 3x - 5y = 7 \) have a unique solution.
Solve the following pair of equations using the cross-multiplication method: \[ 2x + 3y - 46 = 0 \] \[ 3x + 5y - 74 = 0 \]
The simultaneous equations $x + 2y = 70$ and $2x + \lambda y = 35$ have no solution if $\lambda$ will be:
If the pair of linear equations $2x + 3y = 5$ and $4x + ky = 10$ has infinitely many solutions, then the value of $k$ is:
The father is 7 times older than his son. Two years ago, the father was 13 times as old as his son. What are their present ages?
The solution of the pair of linear equations \( x + y = 10 \), \( x - y = 4 \) is:
A fraction becomes \( \frac{1}{3} \) when 1 is subtracted from the numerator and it becomes \( \frac{1}{4} \) when 8 is added to its denominator. Find the fraction.
One third of any number is equal to 21. Then the number will be: