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By: soonteck_01 (offline)  Sunday, February 09 2014 @ 01:18 AM CST (Read 716 times)  
soonteck_01

Q1. x+y/3=x-y/5=2x-3y+5
Solve for x and y

Q2. If x=3 and y=-1 is the solution of the simultaneous equations

3px+qy=11
-qx+5y=p
find the value of p and q

Thanks in advance

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By: echeewh (offline)  Sunday, February 09 2014 @ 09:54 PM CST  
echeewh

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

=========

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

==========

Trust the above helps.

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

Cheers,
Edward



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