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Pair of Linear Equations in Two Variables
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28/05/2021 10:31 am
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Solve the following pairs of equations by reducing them to a pair of linear equations:
1/2x + 1/3y = 2
1/3x + 1/2y = 13/6
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28/05/2021 10:33 am
Let us assume 1/x = m and 1/y = n, then the equation will change as follows.
m/2 + n/3 = 2
⇒ 3m + 2n - 12 = 0…………………….(1)
m/3 + n/2 = 13/6
⇒ 2m+3n-13 = 0……………………….(2)
Now, using cross-multiplication method, we get,
m/(-26-(-36) ) = n/(-24-(-39)) = 1/(9-4)
m/10 = n/15 = 1/5
m/10 = 1/5 and n/15 = 1/5
So, m = 2 and n = 3
1/x = 2 and 1/y = 3
x = 1/2 and y = 1/3