Hey <soonteck_01>

This is not Primary maths that you are asking. And I'm afraid you are putting your questions in the wrong category as always.

Anyway following are my worked solutions ....

Q1

Form 2 equations with x,y in it and apply the Simultaneous method to solve it (since there are only 2 variables x and y)

x+y/3=x-y/5

5(x+y) = 3(x-y)

5x + 5y = 3x - 3y

5x + 5y - 3x + 3y = 0

2x + 8y = 0 -- (1)

x-y/5=2x-3y+5

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

x - y = 10x - 15y + 25

x - y - 10x + 15y = 25

14y - 9x = 25 -- (2)

Eliminating x, multiply (1) 9x, (2) 2x as follows:

(1)x9:

18x + 72y = 0 -- (3)

(2)x2:

28y - 18x = 50 -- (4)

Comparing (3),(4)

(3)+(4):

72y + 28y = 50

100y = 50

y = 5/10 = **1/2**

Sub y into (1), we have ...

2x + 8(1/2) = 0

2x + 4 = 0

2x = -4

x = -(4/2) = **- 2**

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Q2.

9p - q = 11 -- (1)

-3q - 5 = p

-p - 3q = 5 -- (2)

(1)x3:

27p - 3q = 33 -- (3)

(3)-(2):

27p + p = 33 - 5

28p = 28

p = **1**

in (1), we have ...

9(1) - q = 11

q = 9 - 11 = **- 2**

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Trust the above helps.

Do let me know again if this is different from your <Answerkey> or if there's further clarification.

Cheers,

Edward