For what values of P and Q Does the following equations have infinitely many solutions 4x 5y 2?

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 5 years, 4 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

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

For Infinitely many solutions,

{tex}{{{a_1}} \over {{a_2}}} = {{{b_1}} \over {{b_2}}} = {{{c_1}} \over {{c_2}}}{/tex}

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

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

=>     {tex}4p + 32q = 10p + 35q{/tex}

=>     {tex}6p + 3q = 0{/tex}

=>     {tex}2p+q=0{/tex}                ..........(i)

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

=>     {tex}10q - 5p + 5 = 2p + 16q{/tex}

=>     {tex}7p + 6q = 5{/tex}             ............(ii)

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

{tex}p = - 1,q = 2{/tex}