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Pair Of Linear Equations In Two Variables

Question
CBSEENMA10006508
Wired Faculty App

Solve the following pairs of linear equations by the substitution method.

square root of 2 straight x end root plus square root of 3 straight y end root equals 0 square root of 3 straight x end root minus square root of 8 straight y end root equals 0

Solution
square root of 2 straight x end root plus square root of 3 straight y end root equals 0 square root of 3 straight x end root minus square root of 8 straight y end root equals 0
The given pair oflinear eqn. is
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From eq. (ii), we have
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Substituting this value of a in equation (i), we get
square root of 2. fraction numerator square root of 8 over denominator square root of 3 end fraction straight y plus square root of 3 straight y equals 0 rightwards double arrow space fraction numerator 4 over denominator square root of 3 end fraction straight y plus square root of 3 straight y end root equals 0 rightwards double arrow space open parentheses fraction numerator 4 over denominator square root of 3 end fraction plus square root of 3 close parentheses straight y equals 0 rightwards double arrow space space space space space space straight y equals 0
Substituting this value of y in eqn. (iii), we get
straight x equals fraction numerator square root of 8 over denominator square root of 3 end fraction left parenthesis 0 right parenthesis equals 0

Therefore, the solution is

x = 0, y = 0

Verification. Substituting x = 0 and y = 0, we find that both the equation (i) and (ii) are satisfied as shown below :
square root of 2 straight x end root plus square root of 3 straight y end root equals square root of 2 left parenthesis 0 right parenthesis plus square root of 3 left parenthesis 0 right parenthesis equals 0 square root of 3 straight x end root minus square root of 8 straight y end root equals square root of 3 left parenthesis 0 right parenthesis minus square root of 8 left parenthesis 0 right parenthesis equals 0
This verifies the solution.

Some More Questions From Pair of Linear Equations in Two Variables Chapter

Which of the following pairs of linear equations are consistent/inconsistent ? Consistent, obtain the solution graphically :

2x + y – 6 = 0,      4x – 2y – 4 = 0

Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.

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