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for which values of p and q will th following pair of linear equations have infinitely many solutions?

4x +5y=2; (2p + 7q)x + (p+8q)y = 2q - p + 1

Posted by Lalith Saran 7 years, 10 months ago

CBSE > Class 10 > Mathematics

2 answers

Shubham Kumar 3 years, 10 months ago

show that one and only one out of n, n+4, n+8, n+12and n+16 is Divisible by 5 where n isany positive integers

0Thank You

Rashmi Bajpayee 7 years, 10 months ago

Given: a₁ = 4, a₂ = 2p + 7q, b₁ = 5, b₂ = p + 8q, c₁ = 2, c₂ = 2q - p + 1

For Infinitely many solutions,

${{{a_1}} \over {{a_2}}} = {{{b_1}} \over {{b_2}}} = {{{c_1}} \over {{c_2}}}$

=> ${4 \over {2p + 7q}} = {5 \over {p + 8q}} = {2 \over {2q - p + 1}}$

Taking, ${4 \over {2p + 7q}} = {5 \over {p + 8q}}$

=> $4p + 32q = 10p + 35q$

=> $6p + 3q = 0$

=> $2p+q=0$ ..........(i)

Again taking, ${5 \over {p + 8q}} = {2 \over {2q - p + 1}}$

=> $10q - 5p + 5 = 2p + 16q$

=> $7p + 6q = 5$ ............(ii)

On solving eq.(i) and (ii), we get

$p = - 1,q = 2$

2Thank You

ANSWER

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