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標題:

～聯立方程２～

發問:

～聯立方程～ 求下列聯立方程的解。 Ｑ１）y = 2x - 3 4x + y = 9 Ｑ２）y - x = 3 2x + y = 24 Ｑ３）x + y = 13 x - 2y = 1 Ｑ４）x - 2y = 2 3x - y = 10

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最佳解答:

Ｑ１）y = 2x - 3 ......(1) 4x + y = 9......(2) Sub. (1) into (2) 4x + (2x - 3) = 9 6x = 12 x = 2 Sub. x = 2 into (1) y = 2(2) - 3 = 1 x = 2, y = 1 Ｑ２）y - x = 3......(1) 2x + y = 24......(2) From (1) : y = x + 3......(3) Sub. (3) into (2) 2x + (x + 3) = 24 3x = 21 x = 7 Sub. x = 7 into (3) y = (7) + 3 = 10 x = 7, y = 10 Ｑ３）x + y = 13......(1) x - 2y = 1......(2) From (2) : x = 2y + 1......(3) Sub. (3) into (1) (2y + 1) + y = 13 3y = 12 y = 4 Sub. y = 4 into (3) x = 2(4) + 1 = 9 x = 9, y = 4 Ｑ４）x - 2y = 2 ......(1) 3x - y = 10 ......(2) From (1) : x = 2y + 2......(3) Sub. (3) into (2) 3(2y + 2) - y = 10 6y + 6 - y = 10 5y = 4 y = 4/5 Sub. y = 4/5 into (3) x = 2(4/5) + 2 = 18/5 x = 18/5, y = 4/5

其他解答:

1)y = 2x - 3(i) 4x + y = 9(ii) From (i),4x=2y+6(iii) Substitute (iii) into (ii) 2y+6+y=9 3y+6=9 3y=9-6 3y=3 y=1 Substitute y=1 into (i) 1=2x-3 2x=1+3 2x=4 x=4/2 x=2 ------------------------------------------------------------------------------------------------------- 2)y - x = 3(i) 2x + y = 24(ii) From (i),y=3+x Substitute (iii) into (ii) 2x+3+x=24 3x+3=24 3x=24-3 3x=21 x=21/3 x=7 Substitute x=7 into (i) y-7=3 y=3+7 y=10 ------------------------------------------------------------------------------------------------------- 3)x + y = 13(i) x - 2y = 1(ii) From (i),x=13-y(iii) Substitute (iii) into (ii) 13-y-2y=1 13-3y=1 -3y=1-13 -3y=-12 y=-12/-3 y=4 Substitute y=4 into (i) x+4=13 x=13-4 x=9 ------------------------------------------------------------------------------------------------------- 4)x - 2y = 2(i) 3x - y = 10(ii) From (i),3x=6+6y(iii) Substitute (iii) into (ii) 6+6y-y=10 6+5y=10 5y=10-6 5y=4 y=4/5 y=0.8 Substitute y=0.8 into (i) x-2 x 0.8=2 x-1.6=2 x=2+1.6 x=3.6 ========================================================= Vocabularies 1)Substitute ... into ...=代 ... 入 ... 2)From ... =從 ...|||||Ｑ１）y = 2x - 3 ----- (1) 4x + y = 9 ----- (2) (2) -(1) : 4x = 12 - 2x 6x = 12 x = 2 再代入(1) y = 2(2) -3 y = 1 方程的解 : x = 2 , y = 1 Ｑ２）y - x = 3 ---- (1) 2x + y = 24 ----(2) (2) - (1) 3x = 21 x = 7 再代入 (1) y - 7 = 3 y = 10 方程的解 : x = 7 , y = 10 Ｑ３）x + y = 13 --- (1) x - 2y = 1 --- (2) (1) - (2) 3y = 12 y = 4 再代入(1) x + 4 = 13 x = 9 方程的解 : x = 9 , y = 4 Ｑ４）x - 2y = 2 ---(1) 3x - y = 10 ---(2) 先把(1) x 3 : 3x - 6y = 6 ---(3) 考慮 (2) - (3) 5y = 4 y = 4/5 代入(1) x - 8/5 = 2 x = 18/5 方程的解 : x = 18/5 , y = 4/5