The graphs of the linear equations 3x-2y=8 and 4x+3y=5 interest at the point P(α, β). What is the value of (2 α - β)?

Let D and E be two points on the side BC of △ABC such that AD = AE and BAD = ∠EAC. If AB = (3x+1) cm, BD=9 cm, AC = 34 cm and EC = (y+1) cm, then the value of (x + y) is:

When positive numbers a, b and c are divided by 13, the remainders are 9, 7 and 10, respectively. What will be the remainder when (a+2b+5c) is divided by 13?

When positive numbers x, y and z are divided by 31, the remainders are 17, 24 and 27, respectively. When (4x-2y+32) is divided by 31, the remainder will be:

 The area (in sq.units) of the triangle formed by the graphs of 8x+3y=24, 2x+8=y and x-axis is:

The graphs of the equations 3x-20y-2=0 and 11x-5y+61=0 intersect at P(a,b). What is the value of (a² + b² — ab)/(a² — b² + ab)?

If $${45\over53}={1\over{a+{1\over b+{1\over c-{2\over 5}}}}}$$  , where a, b and c are positive integers, then what is the value of (4a-b+3c)?

Find the coordinates of the points where the graph 57x-19y=399 cuts the coordinate axes.