Solue the simultanous equation 4xsquare-9ysquare=19 and 2x+3y=1
4x^2 - 9y^2 = 19
2x+3y = 1
since 3y = 1-2x, 9y^2 = (1-2x)^2
and that means
4x^2 - (1-2x)^2 = 19
Now solve for x, and then you can get y
or, since 4x^2 - 9y^2 = (2x-3y)(2x+3y) you have
2x+3y = 1
2x-3y = 19
and solve as usual