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Pair of Linear Equations in Two Variables
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28/05/2021 10:46 am
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Solve the following pairs of equations by reducing them to a pair of linear equations:
6x + 3y = 6xy
2x + 4y = 5xy
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28/05/2021 10:49 am
6x + 3y = 6xy
6/y + 3/x = 6
Let 1/x = m and 1/y = n
=> 6n +3m = 6
=> 3m + 6n-6 = 0 …………………….(i)
2x + 4y = 5xy
=> 2/y + 4/x = 5
=> 2n +4m = 5
=> 4m+2n-5 = 0 ……………………..(ii)
3m + 6n – 6 = 0
4m + 2n – 5 = 0
By cross-multiplication method, we get
m/(-30 –(-12)) = n/(-24-(-15)) = 1/(6-24)
m/-18 = n/-9 = 1/-18
m/-18 = 1/-18
m = 1
n/-9 = 1/-18
n = 1/2
m = 1 and n = 1/2
m = 1/x = 1 and n = 1/y = 1/2
x = 1 and y = 2
Hence, x = 1 and y = 2