Rozwiąż układ równań metodą przeciwnych współczynników i sprawdź poprawność rozwiązania d) {1/3x - 1/2y = 4 {1/2x + 1/4y = 2 e) {2/3m - 2n = 1 {1/2m = 1/2m + 3/4n f) {10a = 2 + 5b {a + b = 0,5

1/3x - 1/2y = 4 // *6 1/2x + 1/4y = 2  //*4 2x - 3y = 24 2x + y = 8  //* (-1) 2x - 3y = 24 -2x - y = -8 -------------------- 2x - 3y -2x - y = 24 - 8 -4y = 16  //: -4 y = -4 1/3x - 1/2y = 4 1/3x - 1/2 *(-4) = 4 1/3x + 2 = 4 1/3x = 2 //*3 x = 6 spr: 1/3 * 6 - 1/2 * (-4) = 2 + 2 = 4     L =P II :  1/2x + 1/4y = 1/2 * 6 + 1/4 * (-4) = 3 - 1 = 2    L=P zaraz podam resztę 2/3m - 2n = 1  //*3 1/2m = 1/2m + 3/4n  //*4 2m - 6n = 3 2m = 2m + 3n  // *2 2m - 6n = 3 4m = 4m + 6n ---------------------- 2m - 6n + 4m + 6n = 3 + 4m 6m = 3 + 4m  //-4m 2m = 3  //:2 m = 3/2 2/3m - 2n = 1 2/3 * 3/2 - 2n = 1 1 - 2n = 1 -2n = 0 n = 0 spr I: 2/3 * 3/2 - 2 * 0 = 1 - 0 = 1    L=P II : P= 1/2 * 3/2 + 0 = 3/4  L = 1/2 * 3/2 = 3/4     L=P 10a = 2 + 5b  //-5b a + b=0,5 10a - 5b = 2 a + b = 0,5 //* 5 10a - 5b = 2 5a + 5b = 2,5 ---------------------- 10a - 5b + 5a + 5b = 2 + 2,5 15a = 4,5 a = 0,3 a + b = 0,5 0,3 + b = 0,5  //- 0,3 b = 0,2 spr: L = 1o * 0,3 = 3    P = 2 + 5 * 0,2 = 2 + 1 = 3   L=P II : 0,3 + 0,2 = 0,5    L=P

1/3x - 1/2y = 4 // *6 1/2x + 1/4y = 2  //*4 2x - 3y = 24 2x + y = 8  //* (-1) 2x - 3y = 24 -2x - y = -8 -------------------- 2x - 3y -2x - y = 24 - 8 -4y = 16  //: -4 y = -4 1/3x - 1/2y = 4 1/3x - 1/2 *(-4) = 4 1/3x + 2 = 4 1/3x = 2 //*3 x = 6 spr: 1/3 * 6 - 1/2 * (-4) = 2 + 2 = 4     L =P II :  1/2x + 1/4y = 1/2 * 6 + 1/4 * (-4) = 3 - 1 = 2    L=P zaraz podam resztę 2/3m - 2n = 1  //*3 1/2m = 1/2m + 3/4n  //*4 2m - 6n = 3 2m = 2m + 3n  // *2 2m - 6n = 3 4m = 4m + 6n ---------------------- 2m - 6n + 4m + 6n = 3 + 4m 6m = 3 + 4m  //-4m 2m = 3  //:2 m = 3/2 2/3m - 2n = 1 2/3 * 3/2 - 2n = 1 1 - 2n = 1 -2n = 0 n = 0 spr I: 2/3 * 3/2 - 2 * 0 = 1 - 0 = 1    L=P II : P= 1/2 * 3/2 + 0 = 3/4  L = 1/2 * 3/2 = 3/4     L=P 10a = 2 + 5b  //-5b a + b=0,5 10a - 5b = 2 a + b = 0,5 //* 5 10a - 5b = 2 5a + 5b = 2,5 ---------------------- 10a - 5b + 5a + 5b = 2 + 2,5 15a = 4,5 a = 0,3 a + b = 0,5 0,3 + b = 0,5  //- 0,3 b = 0,2 spr: L = 1o * 0,3 = 3    P = 2 + 5 * 0,2 = 2 + 1 = 3   L=P II : 0,3 + 0,2 = 0,5    L=P