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Pair of Linear Equations in Two Variables
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28/05/2021 10:57 am
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Solve the following pairs of equations by reducing them to a pair of linear equations:
1/(3x+y) + 1/(3x-y) = 3/4
1/2(3x+y) – 1/2(3x-y) = -1/8
1 Answer
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28/05/2021 10:58 am
Substituting 1/(3x+y) = m and 1/(3x-y) = n in the given equations, we get,
m + n = 3/4 …………….…… (1)
m/2 – n/2 = -1/8
m – n = -1/4 …………..…(2)
Adding (1) and (2), we get
2m = 3/4 – 1/4
2m = 1/2
Putting in (2), we get
1/4 – n = -1/4
n = 1/4 + 1/4 = 1/2
m = 1/(3x+y) = 1/4
3x + y = 4 ……………………(3)
n = 1/( 3x-y) = 1/2
3x – y = 2 …………………(4)
Adding equations (3) and (4), we get
6x = 6
x = 1 ………………….(5)
Putting in (3), we get
3(1) + y = 4
y = 1
Hence, x = 1 and y = 1