Show that the system of equations
` 3x - 5y = 7, 6x - 10 y = 3 `.
has no solution.

Explanation

The given system of equations is
` 3x - 5y - 7 = 0 and 6 x - 10 y - 3 = 0 `
These equations are of the form
` a_ 1 x + b_ 1 y + c_ 1 = 0 and a _ 2 x + b_ 2 y + c _ 2 = 0 ` ,
where ` a_ 1 = 3, b_ 1 = - 5, c_ 1 = - 7 and a_ 2 = 6, b_ 2 = - 10, c_ 2 = -3`
` therefore (a_ 1 ) /(a_ 2) = ( 3) /(6) = (1)/(2), (b_ 1 ) /(b_ 2 ) = (-5)/(-10) = (1)/(2) and (c_ 1 ) /(c_ 2 ) = (-7)/(-3) = ( 7) /(3)`
Clearly, `(a_ 1 ) /(a_ 2 ) = (b_1) /(b_ 2 ) ne (c_ 1 ) /(c_ 2) `
Hence, the given system of equations has no soluion.