Solve the following system of equations by using the method of cross multiplication
2x + 3y = 7 and 6x + 5y = 11.

Explanation

The given equations can be written as 2x + 3y - 7 = 0
and 6x + 5y - 11 = 0
By cross multiplication method, we get

`(x)/(3xx(-11) - 5 xx (-7)) = (y)/(-7 xx 6 - (-11)xx2) = (1)/(2xx5 - 6 xx 3)`
implies `(x)/(-33+35) = (y)/(-42 + 22) = (1)/(10-18)`
implies `(x)/(2) = (y)/(-20) = (1)/(-8)`
when `(x)/(2) = - (1)/(8) or x = - (1)/(4)`
and `(y)/(-20) = - (1)/(8) or y = (20)/(8) = (5)/(2)`
Hence, `{:(x = - (1)/(4)),(y = (5)/(2)):}}"is the required solution"`.