The lines joining locations with equal shaking intensity

Find the value of 'a' and 'b' which satisfy the following equations:

9a + 7b = 30

4a - 5b = 62

Find the area between the lines 18x +12y = 108, 9x  + 6y  = 27, x - axis and y -axis. 

If (5√P - 7√Q) = 5, [1.5P = 4Q-(R/3)+9] and (√P/√Q) = 1.6, then find out the value of ‘R’.

I. p² – 5p + 6 = 0                  

II. 36q² = 81

The slope of the equation  24x+ 8y =56 is

The ratio of roots of the equation mx² + nx + n = 0 is α/ β = a/b, then find the value of `sqrt(a/b)+sqrt(b/a)+sqrt(n/m)`

The equations 6x + my + 18 = 0 and 9x + 21y + 27 = 0 have a unique solution. Which of the following statements is definitely true?

If in two linear equations ax + by = c and dx + ey = f and a/d = b/e = c/f  then, which of the following is true about the two equations?

I. p² - 365 = 364

II. q - √ 529 = √ 169