問3題數學題~

Question

solve the following simultaneous equation

1.3x-1=4(y+1)

7(2x+3)=6y

2.(x+9)/3-(y-10)/2=4

x+5y/2=4

3.6x+10y=600

35x=25y

Answer 1

3x-1=4(y+1)..............(1)
7(2x+3)=6y...............(2)

From (1),
3x - 1 = 4y + 4
3x - 4y = 5
9x - 12y = 15................(3)

From (2),
14x + 21 = 6y
14x - 6y = -21
28x - 12y = -42..............(4)

(3) - (4)
9x - 28x - 12y + 12y = 15 + 42
-19x = 57
x = -3 //

Sub. x = -3 into (3)
-27 - 12y = 15
-12y = 42
y = -42/12
y = -7/2 //

The solution is x = -3, y = -7/2.

2.
(x+9)/3-(y-10)/2=4.............(1)
x+5y/2=4.........................(2)

From (1),
2( x+9 ) - 3( y-10 ) = 24
2x + 18 -3y + 30 = 24
2x - 3y = -24.....................(3)

From (2),
2x + 5y = 8.......................(4)

(4) - (3)
2x + 5y - 2x + 3y = 8 + 24
8y = 32
y = 4 //

Sub. y = 4 into (4)
2x + 20 = 8
2x = -12
x = -6 //

The soluition is x = -6, y = 4

3.
6x+10y=600...............(1)
35x=25y ....................(2)

From (1)
3x + 5y = 300
15x + 25y = 1500.........(3)

Sub (2) into (3)
15x + 35x = 1500
50x = 1500
x = 30 //

Sub x = 30 into (2)
1050 = 25y
y = 42 //

The solution is x = 30, y = 42

Answer 2

1. 4 2.3 3.6