～聯立方程２～

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

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
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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
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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
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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
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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