Odpowiedź:
[tex]a) \\ x + 3y = 3 \\ x - y = 5 \\ \\ x = 3 - 3y \\ 3 - 3y - y = 5 \\ \\ x = 3 - 3y \\ 3 - 4y = 5 \\ \\ x = 3 - 3y \\ - 4y = 5 - 3 \\ \\ x = 3 - 3y \\ 4y = - 2 \\ \\ x = 3 - 3y \\ y = - \frac{ 1}{2} \\ \\ x = 3 - 3 \times ( - \frac{1}{2} ) \\ y = - \frac{1}{2} \\ \\ x = 4 \frac{1}{2} \\ y = - \frac{1}{2} [/tex]
[tex]b) \\ 2x - y = 10 \\ x + 5y = - 17 \\ \\ 2x - y = 10 \\ x = - 17 - 5y \\ \\ 2( - 17 - 5y) - y = 10 \\ x = - 17 - 5y \\ \\ - 34 - 10y - y = 10 \\ x = - 17 - 5y \\ \\ - 11y = 10 + 34 \\ x = - 17 - 5y \\ \\ - 11y = 44 \\ x = - 17 - 5y \\ \\ y = - 4 \\ x = - 17 - 5 \times ( - 4) \\ \\ y = - 4 \\ x = - 17 + 20 \\ \\ y = - 4 \\ x = 3[/tex]
[tex]c) \\ 3m + n = 9 \\ 2m - 5n = - 11 \\ \\ n = 9 - 3m \\ 2m - 5(9 - 3m) = - 11 \\ \\ n = 9 - 3m \\ 2m - 45 + 15m = - 11 \\ \\ n = 9 - 3m \\ 17m = 34 \\ \\ n = 9 - 3m \\ m = 2 \\ \\ n = 9 - 3 \times 2 \\ m = 2 \\ \\ n = 3 \\ m = 2[/tex]
[tex]d) \\ 4a - 2 = b \\ 3a + 7b = 1.5 \\ \\ b = 4a - 2 \\ 3a + 7(4a - 2) = 1.5 \\ \\ b = 4a - 2 \\ 3a + 28a - 14 = 1.5 \\ \\ b = 4a - 2 \\ 31a = 15.5 \\ \\ b = 4a - 2 \\ a = \frac{15.5}{31} \\ \\ b = 4a - 2 \\ a = \frac{1}{2} \\ \\ b = 4 \times \frac{1}{2} - 2 \\ a = \frac{1}{2} \\ \\ b = 0 \\ a = 2[/tex]
[tex]e) \\ 5x = 4 - 2y \\ 4x + y = 3 \\ \\ 5x = 4 - 2y \\ y = 3 - 4x \\ \\ 5x = 4 - 2(3 - 4x) \\ y = 3 - 4x \\ \\ 5x = 4 - 6 + 8x \\ y = 3 - 4x \\ \\ 5x - 8x = - 2 \\ y = 3 - 4x \\ \\ - 3x = - 2 \\ y = 3 - 4x \\ \\ x = \frac{2}{3} \\ y = 3 \frac{8}{3} \\ \\ x = \frac{2}{3} \\ y = \frac{1}{3} [/tex]
[tex]f) \\ 6x - 3y = 9 \\ x + 5y = - 9.5 \\ \\ 6x - 3y = 9 \\ x = - 9.5 - 5y \\ \\ 6( - 9.5 - 5y) - 3y = 9 \\ x = - 9.5 - 5y \\ \\ - 57 - 30y - 3y = 9 \\ x = - 9.5 - 5y \\ \\ - 33y = 66 \\ x = - 9.5 - 5y \\ \\ y = - 2 \\ x = - 9.5 - 5 \times ( - 2) \\ \\ y = - 2 \\ x = \frac{1}{2} [/tex]
