Maths 1 Marks Question

Solve for x and y:
23x + 24y = 23
24x + 23y = 24

Sum of two numbers is 105 and their difference is 45. Find the numbers.

If 2x + y = 13 and 4x - y = 17, find the value of (x - y).

Write the value of k for which the system of equations x + y- 4 = 0 and 2x + ky - 3 = 0 has no solution.

Write the number of solutions of the following pair of linear equations:
x+3y -4 = 0
2x +6y = 7

Write the number of solutions of the following pair of linear equations:
x+ 2y-8= 0
2x + 4y = 16

For what value of k, the following pair of linear equations has infinitely many solutions?
10x + 5y - (k - 5) == 0
20x + 10y - k = 0

Write the set of values of a and b for which the following system of equations has infinitely many solutions.
2x + 3y = 7
2ax + (a + b) y == 28

Write the values of k for which the system of equations x + ky = 0, 2x - y = 0 has unique solution.

Write the value of k for which the system of equations 3x - 2y = 0 and kx + 5y = 0 has infinitely many solutions.