Solve the simultaneous equations, 2x+y-5=0 and x^2-y^2=3
2x+y-5=0, y=5-2x (put into second equation)
x2-y2=3, substituting in we get, x2-(5-2x)2=3, expand, x2-(25+4x2-20x)=3, simplify, x2-25-4x2+20x=3, 0=3x2-20x+28, put into brackets by seperating the two factors, 0=3x2-6x-14x+28, 0=(3x-14)(x-2), therefore x=14/3 and x=2, y=1 and y=-13/3
Solved.
