method of substitution

您好，我是 lop，高興能解答您的問題。

(1)

9x = 8y - 1 --- (1)
6x - 4y = 0 --- (2)

From (2) :

6x = 4y
x = 2y/3 --- (3)

Sub. (3) into (1)

9(2y/3) = 8y - 1
6y = 8y - 1
y = 1/2 --- (4)

Sub. (4) into (3)

x = 1/3

Answer : x = 1/3 , y = 1/2 .

(2)

10y + 6x = -1 --- (1)
2x + 5y = 0 --- (2)

From (2) :

2x = -5y
x = -5y/2 --- (3)

Sub. (3) into (1)

10y + 6(-5y/2) = -1
10y - 15y = -1
-5y = -1
y = 1/5 --- (4)

Sub. (4) into (3)

x = -1/2

Answer : x = -1/2 , y = 1/5 .

(3)

3x = 8y - 3 --- (1)
9x + 16y = 1 --- (2)

From (1) :

x = (8y-3)/3 --- (3)

Sub. (3) into (2)

9(8y-3)/3 + 16y = 1
24y - 9 + 16y = 1
40y = 10
y = 1/4 --- (4)

Sub. (4) into (3)

x = [8(1/4)-3]/3
x = (2-3)/3
x = -1/3

Answer : x = -1/3 , y = 1/4 .

(4)

x + y = 3 --- (1)
5y - 5x = 7 --- (2)

From (1) :

x = 3-y --- (3)

Sub. (3) into (2)

5y - 5(3-y) = 7
5y - 15 + 5y = 7
10y = 22
y = 22/10
y = 11/5 --- (4)

Sub. (4) into (3)

x = 3-11/5
x = 4/5

Answer : x = 4/5 , y = 11/5 .

(1)
9x = 8y - 1 --- (1)
6x - 4y = 0 --- (2)
From (2) :
6x = 4y
x = 2y/3 --- (3)
Sub. (3) into (1)
9(2y/3) = 8y - 1
6y = 8y - 1
y = 1/2 --- (4)
put y=0.5 into (3)
x=2(0.5)/3X=1/3
so(x,y)=(1/3,0.5)

(2)
10y + 6x = -1 --- (1)
2x + 5y = 0 --- (2)
From (2) :
2x = -5y
x = -5y/2 --- (3)
put (3) into (1)
10y + 6(-5y/2) = -1
10y - 15y = -1
-5y = -1
y = 1/5
put y=0.2 into (3)
x=-5(0.2)/2X=-0.5
so(x,y)=(-0.5,0.2)
(3)
3x = 8y - 3 --- (1)
9x + 16y = 1 --- (2)
From (1) :
x = (8y-3)/3 --- (3)
put (3) into (2)
9(8y-3)/3 + 16y = 1
24y - 9 + 16y = 1
40y = 10
y = 0.25
put y=0.25 into (3)
x = [8(0.25)-3]/3
x = -1/3
so (x,y)=(-1/3,0.25)
(4)
x + y = 3 --- (1)
5y - 5x = 7 --- (2)
From (1) :
x = 3-y --- (3)
put (3) into (2)
5y - 5(3-y) = 7
5y - 15 + 5y = 7
10y = 22
y =2.2
put y=11/5 into (3)
x = 3-11/5
x =0.8
so(x,y)=(0.8,11/5)