Rozwiąż układ równań: 1) { 6a+9b=126 2(6+a+9+b)=54 { 6a+9b=126 /:6 12+2a+18+2b=54 { a+1,5b=21 /*(-1) 2a+2b=24 /:2 { -a-1,5b=-21 a+b=12 --------------- -1/2b=-9 b=18 a=-6 2) {1/2x-3/4y=0 /*4 2/3x+1 1/4y=9 /*12 {2x-3y=0 /*5 8x+15y=108 {10x-15y=0 8x+15y=108 -------------- 18x=108 x=6 y=4 3) { 3x+4y=5/3 *(-3) 6x+3y= 5/4 /*4 -9x-12y=-5 24x+12y=5 ----------------- 15x=0 x=0 y=5/12
1) { 6a+9b=126 2(6+a+9+b)=54 6a + 9b = 126 12 + 2a + 18 + 2b = 54 6a + 9b = 126 2a + 2b = 54 - 12 - 18 6a + 9b = 126 2a + 2b = 24 2a = 24 - 2b |:2 a = 12 - b 6(12 - b) + 9b = 126 72 - 6b + 9b = 126 -6b + 9b = 126 - 72 3b = 54 |:3 b = 18 a = 12 - b a = 12 - 18 a = -6 2) {1/2x-3/4y=0 2/3x+1 1/4y=9 ½x - ¾y = 0 ⅔x + 1 ¼y = 9 ½x - ¾y = 0 |*5 ⅔x + 5/4y = 9 |*3 5/2x - 15/4y = 0 6/3x + 15/4y = 27 5/2x + 6/3x = 27 15/6x + 12/6x = 27 27/6x = 27 |*6 27x = 162 |:27 x = 6 1/2x - 3/4y = 0 3 - 3/4y = 0 -3/4y = -3 |*(-4) 3y = 12 |:3 y = 4 3) { 3x+4y=1 2/3 |*2 6x+3y= 1 1/4 6x + 8y = 5/3 * 2 6x + 3y = 1 ¼ 6x + 8y = 10/3 6x + 3y = 1¼ 6x = 10/3 - 8y podstawiamy: 10/3 - 8y + 3y = 1¼ -8y + 3y = 1¼ - 10/3 -5y = 5/4 - 10/3 -5y = 15/12 - 50/12 -5y = -35/12 |:(-5) y = 35/12 * ⅕ y = 35/60 y = 7/12 6x = 10/3 - 8y 6x = 10/3 - 8*7/12 6x = 10/3 - 56/12 6x = 40/12 - 56/12 6x = -16/12 6x = - 4/3 |:6 x = -4/3 * ⅙ x = -4/18 x = -2/9
