What are the points of intersection of the equations of 3x minus 2y equals 1 and 3x squared minus 2y squared plus 5 equals 0 showing details of your work?

A: 3x-2y = 1 => 3x = 1+2y

B: 3x2-2y2+5 = 0 => 3x2 = 2y2-5

Square both sides in equation A: 9x2 = 1+4y+4y2

Multiply all terms by 3 in equation B: 9x2 = 6y2-15

So it follows that:-

6y2-15 = 1+4y+4y2 and 6y2-15-1-4y-4y2 = 0

Collect like terms: 2y2-4y-16 = 0

Divide all terms by 2: y2-2y-8 = 0

Factorise: (y-4)(y+2) = 0

Therefore: y = 4 or y = -2

Substitute the above y values into the linear equation to find the values of x:

The points of intersection are: (3, 4) and (-1,-2)