Odpowiedź:
zad. 20
[tex] \frac{2}{3} - x = \frac{1}{4} \\ - x = \frac{1}{4} - \frac{2}{3} \\ - x = \frac{3}{12} - \frac{8}{12} \\ - x = - \frac{5}{12} \\ x = \frac{5}{12} [/tex]
zad. 21
[tex] \frac{1}{5} + x = \frac{4}{5} \\ x = \frac{4}{5} - \frac{1}{5} \\ x = \frac{3}{5} [/tex]
zad. 22
[tex]a. \\ 3x - 2y = 8 \\ 2x + y = 3 \\ \\ 3x - 2y = 8 \\ y = 3 - 2x \\ \\ 3x -2(3 - 2x) = 8 \\ y = 3 - 2x \\ \\ 3x - 6 + 4x = 8 \\ y = 3 - 2x \\ \\ 7x = 14 \\ y = 3 - 2x \\ \\ x = 2 \\ y = 3 - 2 \times 2 \\ \\ x = 2 \\ y = 3 - 4 \\ \\ x = 2 \\ y = - 1[/tex]
[tex]b. \\ 2(x + y) - 3(x + 2) = 2 \\ 3(x - y) + 2(y + 2) = 2x - 1 \\ \\ 2x + 2y - 3x - 6 = 2 \\ 3x - 3y + 2y + 4 = 2x - 1 \\ \\ - x + 2y = 8 \\ x - y = - 5 \\ \\ x = - 8 + 2y \\ - 8 + 2y - y = - 5 \\ \\ x = - 8 + 2y \\ y = 3 \\ \\ x = - 8 + 6 \\ y = 3 \\ \\ x = - 2 \\ y = 3[/tex]
[tex]c. \\ x + y = 1 \\ 5x - y = 0 \\ \\ 6x = 1 \\ x = \frac{1}{6} \\ \\ \frac{1}{6} + y = 1 \\ y = \frac{5}{6} [/tex]
[tex]d. \\ x + 4y - 0.75 = 2.5 + 0.5y - 2x \\ 3y - x = 2y + 0.5x - 0.25 \\ \\ x + 2x + 4y - 0.5y = 2.5 + 0.75 \\ - x - 0.5x + 3y - 2y = - 0.25 \\ \\ 3x + 3.5y = 3.25 \\ - 1.5x + y = - 0.25 \\ \\ 3x + 3.5y = 3.25 \\ y = - 0.25 + 1.5x \\ \\ 3x + 3.5( - 0.25 + 1.5x) = 3.25 \\ y = - 0.25 + 1.5x \\ \\ 3x - 0.875 + 5.25x = 3.25 \\ y = - 0.25 + 1.5x \\ \\ 8.25x = 4.125 \\ y = - 0.25 + 1.5x \\ \\ x = \frac{1}{2} \\ y = - 0.25 + \frac{3}{4} \\ \\ x = \frac{1}{2} \\ y = \frac{1}{2} [/tex]
zad. 23
[tex]x + y = - 40 \\ x - y = - 60 \\ \\ 2x = - 100 \\ x = - 50 \\ \\ - 50 + y = - 40 \\ y = - 40 + 50 \\ y = 10[/tex]
