Algebraic Methods of Solving a Pair of Linear Equations - Cross - Multiplication Method

Solve each of the following systems of equations by the method of cross-multiplication 

`x/a = y/b`

`ax + by = a^2 + b^2`

Solve the following system of equations in x and y by cross-multiplication method

`(a – b) x + (a + b) y = a^2 – 2ab – b^2`

`(a + b) (x + y) = a^2 + b^2`

Solve the following systems of equations:

`sqrt2x + sqrt3y = 0`

`sqrt3x - sqrt8y = 0`

A two-digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting 5 or by multiplying the difference of the digits by 16 and then adding 3. Find the number.

Solve the following systems of equations:

`1/(7x) + 1/(6y) = 3`

`1/(2x) - 1/(3y) = 5`

Solve the following systems of equations:

`1/(2x) + 1/(3y) = 2`

`1/(3x) + 1/(2y) = 13/6`

Solve each of the following systems of equations by the method of cross-multiplication 

`x/a + y/b = a + b`

A thief, after committing a theft, runs at a uniform speed of 50 m/minute. After 2 minutes, a policeman runs to catch him. He goes 60 m in first minute and increases his speed by 5 m/minute every succeeding minute. After how many minutes, the policeman will catch the thief?