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  • Find the solution of the pair of equation x by 10 plus y by 5– 1 = 0 and x by 8 plus y by 6=15 . Hence, find lambda, if y = lambdax + 5.

Find the solution of the pair of equation \frac{x}{10}+\frac{y}{5}-1= 0 and \frac{x}{8}+\frac{y}{6}= 15.

Hence, find \lambda, if y = \lambdax + 5.

Answers (1)

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Solution:

\frac{x}{10}+\frac{y}{5}= 1\Rightarrow \frac{x+2y}{10}= 1\Rightarrow x + 2y = 10 …(1)

\frac{x}{8}+\frac{y}{6}= 15\Rightarrow \frac{3x+4y}{24}= 15\Rightarrow  3x + 4y = 360 … (2)

Multiply eq. (1) by 2 and subtract from eq. (2) we get
3x – 2x = 360 – 20.
x = 340
Put x = 340 in eq. 1 we get
340 + 2y = 10
2y = 10 – 340
y = -\frac{330}{2}
y = – 165
y = \lambdax + 5
Put x = 340 and y = –165 we get
–165 = \lambda(340) + 5
–170 = \lambda(340)

\lambda = \frac{-1}{2}

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infoexpert27

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