3.3.1 Sistem Persamaan, soalan panjang (Soalan 1 & 2)

3.3.1 SPM Praktis, Sistem Persamaan, (Soalan panjang)

Soalan 1:

Selesaikan persamaan serentak.

\begin{array}{l} y + 2 x = 2 \\ \frac{2}{x} + \frac{1}{y} = 5 \end{array}

Penyelesaian:

\begin{array}{l} y + 2 x = 2 - - - - (1) \\ \frac{2}{x} + \frac{1}{y} = 5 - - - - (2) \\ y = 2 - 2 x - - - - (3) \\ Gantikan (3) ke dalam (2), \\ \frac{2}{x} + \frac{1}{2 - 2 x} = 5 \\ \frac{2 (2 - 2 x) + x}{x (2 - 2 x)} = 5 \\ 4 - 4 x + x = 5 x (2 - 2 x) \\ 4 - 3 x = 10 x - 10 x^{2} \\ 10 x^{2} - 13 x + 4 = 0 \\ (5 x - 4) (2 x - 1) = 0 \\ 5 x - 4 = 0 atau     2 x - 1 = 0 \\ x = \frac{4}{5} atau x = \frac{1}{2} \\ Gantikan nilai-nilai x ke dalam (3), \\ Apabila x = \frac{4}{5}, \\ y = 2 - 2 (\frac{4}{5}) = \frac{2}{5} \\ Apabila x = \frac{1}{2} \\ y = 2 - 2 (\frac{1}{2}) = 1 \\ Penyelesaian ialah x = \frac{4}{5}, y = \frac{2}{5} dan x = \frac{1}{2}, y = 1. \end{array}

Soalan 2:

Selesaikan persamaan serentak.

x – 3y + 5 = 3y + 5y²– 6 – x = 0

Penyelesaian:

x – 3y + 5 = 0

x = 3y – 5 —–(1)

3y + 5y² – 6 – x = 0 —–(2)

Gantikan (1) ke dalam (2),

3y + 5y² – 6 – (3y – 5) = 0

3y + 5y² – 6 – 3y + 5 = 0

5y² – 1 = 0

5y² = 1

y = 0.447

Gantikan nilai-nilai y ke dalam (1),

Apabila y = 0.447

x = 3 (0.447) – 5

x = –3.659

Apabila y = – 0.447

x = 3 (–0.447) – 5

x = –6.341

Penyelesaian ialah x = –3.659, y = 0.447 dan x = –6.341, y = – 0.447.