An cearcallTuilleadh eisimpleirean de thrasnaidhean

\(y = 2x + 1\)

\({x^2} + {y^2} - 6x - 7y + 9 = 0\)

\({x^2} + {(2x + 1)^2} - 6x - 7(2x + 1) + 9 = 0\)

\({x^2} + 4{x^2} + 4x + 1 - 6x - 14x - 7 + 9 = 0\)

\(5{x^2} - 16x + 3 = 0\)

\((5x - 1)(x - 3) = 0\)

\(x = \frac{1}{5},3\)

\(y = \frac{7}{5},7\)

Mar sin tha an loidhne \(2x + 1\) a' trasnadh a' chearcaill aig \(\left( {\frac{1}{5},\frac{7}{5}} \right)\) agus \((3,7)\).

\(3y = 2x - 8\)

\(y = \frac{2}{3}x - \frac{8}{3}\)

\({x^2} + {y^2} - 4x - 6y = 0\)

\({x^2} + {\left( {\frac{2}{3}x - \frac{8}{3}} \right)^2} - 4x - 6\left( {\frac{2}{3}x - \frac{8}{3}} \right) = 0\)

\({x^2} + \frac{4}{9}{x^2} - \frac{{32}}{9}x + \frac{{64}}{9} - 4x - 4x + 16 = 0\)

\(9{x^2} + 4{x^2} - 32x + 64 - 36x - 36x + 144 = 0\)

\(13{x^2} - 104x + 208 = 0\)

\(13({x^2} - 8x + 16) = 13(x - 4)(x - 4) = 0\)

\(x = 4\) sin freumhan co-ionann. \(y = 0\)

Tha an loidhne a' suathadh sa chearcall aig \((4,0)\).

\(y = 2x - 8\)

\({x^2} + {y^2} - 2x - 2y - 3 = 0\)

\({x^2} + {(2x - 8)^2} - 2x - 2(2x - 8) - 3 = 0\)

\({x^2} + 4{x^2} - 32x + 64 - 2x - 4x + 16 - 3 = 0\)

\(5{x^2} - 38x + 77 = 0\)

\({b^2} - 4ac = {( - 38)^2} - 4 \times 5 \times 77 = - 96\)

\({b^2} - 4ac\) àicheil, agus mar sin chan eil freumhan fìor ann.

Mar sin tha an loidhne \(y = 2x - 8\) a' seachnadh a' chearcaill.