The chapter is about (Simultaneous Linear Equations in Two Unknows)

I Have 2 questions to ask.

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

2.There are two sections in a Mathematics test.Each correct answer in Section A scores 2 marks, while each in section B scores 3 marks.If Johnny has answerd 40 questions correctly and scored 92 marks, find the number of questions he has answerd correctly in Section A and B respectively.

**THX

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1 十年 前
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1.

x+9/3 - y-10/2= x+5y/2=4

(x + 5y)/2 = 4

x + 5y = 8

x = 8 - 5y---------------(1)

x+9/3 - y-10/2 = 4

2(x + 9) - 3(y + 10) = 24

2x + 18 - 3y - 30 = 24

2x - 3y = 36----------------(2)

sub (1) into (2)

2(8 - 5y) - 3y = 36

16 - 10y - 3y = 36

-13y = 20

y = - 20/13

sub y = -20/13 into (1)

x = 8 - 5( - 20/13)

13x = 104 + 100

13x = 204

x = 204/13

so, x = 204/13,y = - 20/13

2).There are two sections in a Mathematics test.Each correct answer in Section A

scores 2 marks, while each in section B scores 3 marks.If Johnny has answerd 40

questions correctly and scored 92 marks, find the number of questions he has

correctly in Section A and B respectively.

Let x and y be the number of question that he has answered correctly in Section A and

B respectively,

2x + 3y = 92----------------(1)

x + y = 40----------------(2)

(2) x 2:

2x +2y = 80

(1) - (2):

y = 12

sub y = 12 into (2)

x = 28

so,he has answerd correctly 28 questions in Section A and 12 questions in Section B

respectively.

資料來源： by eason mensa
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• 1.the simultaneous equations can be rewritten as:(跟足Format)

{x+9/3 - y-10/2=4_____(1)

{x+5y/2=4________(2)

From (2), we get that x=4-5y/2______(3)

Substitute (3) into (1),

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

(8-5y+18+3y+30)/6=4

56-2y=6x4

56-24=2y

y=16.

Substitute y=16 into (3),

x=4-5(16)/2

=-38

So the solution is x=-38, y=16.(唔知啱唔啱)

2.Let x be the number of questions in Section A that Johnny has answered correctly, then the number of questions in Section B that Johnny has answered correctly is 40-x.

2x+3(40-x)=92

2x+120-3x=92

120-92=3x-2x

so x=28.

The number of questions in Section A that Johnny has answered correctly is 28,and the number of questions in Section B that Johnny has answered correctly is 40-28=12 questions.(唔知啱唔啱)

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