Solve the following system of equations by cross multiplication method
3x - 5y = 20 and 7x + 2y = 17.

Explanation

The given equations can be written as
3x - 5y - 20 = 0
and 7x + 2y - 17 = 0
By cross multiplication method, we have

`(x)/((-5)xx(-17)-2xx(-20)) = (y)/((-20) xx 7 - (-17) xx3) = (1)/(3xx2 - 7 xx (-5))`
implies `(x)/(85 + 40) = (y)/(-140 + 51) = (1)/(6 + 35)`
implies `(x)/(125) = (y)/(-89) = (1)/(41)`
when `(x)/(125) = (1)/(41) implies x = (125)/(41)`
and `(y)/(-89) = (1)/(41) implies y = - (89)/(41)`
Hence, `{:(x = (125)/(41)),(y = - (89)/(41)):}}` is the required solution.