What are the solutions to the simultaneous equations of 3x -2y equals 1and 3x squared -2y squared plus 5 equals 0 showing work?

If: 3x-2y = 1

Then: 9x^2 = (1+2y)^2 by squaring both sides

If: 3x^2 -2y^2 +5 = 0

Then: 9x^2 = 6y^2 -15 by multiplying all terms by 3

So: 6y^2 -15 = 1+4y +4y^2

Transposing and collecting like terms: 2y^2 -16 -4y = 0

Divide all terms by two: y^2 -8 -2y = 0

Factorizing: (y-4)(y+2) = 0 => y = 4 or y = -2

Therefore solutions by substitution are: (3, 4) and (-1, -2)