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Question

Question 1 (i)
Solve the following pairs of equations by reducing them to a pair of linear equations:

12x+13y=2
13x+12y=136

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Solution

12x+13y=2
13x+12y=136
Let 1x=p and 1y=q, then the equations changes as below:
p2+q3=2
3p+2q12=0 ... (i)
p3+q2=136
2p+3q13=0 ... (ii)

Compare the given equations with

a1x+b1y+c1=0 and a2x+b2y+c2=0.

By cross-multiplication method, we get

xb1c2b2c1=yc1a2c2a1=1a1b2a2b1
p26(36)=q24(39)=194
p10=q15=15
p10=15 and q15=15
p=2 and q=3
1x=2 and 1y=3
Hence, x=12 and y=13


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