Question

Find p and q if equations 2x + 3y = 7 ; (p + q)x + (2p - q)y = 21. Represent coincident lines

Answer 1

$Heya$‼

As we know,
Condition for coincident lines :-
$a1/a2=b1/b2=c1/c2$

Given equations :-
$2x+3y=7$ ...(1)
$(p+q)x+(2p-q)y=21$ ...(2)

Now. according to the condition for coincident lines :

$2/(p+q)=3/(2p-q)=7/21$

$2/(p+q)=3/(2p-q)$ $and$ $3/(2p-q)=1/3$

$2(2p-q)=3(p+q)$ $and$ $3×3=2p-q$

$4p-2q=3p+3q$ $and$ $6=2p-q$

$4p-3q=3q+2q$ $and$ $2p-q=6$


$q=5p$ ...(1)
$and$
$2p-q=6$ ...(2)



Substituting $q=5p$ in (2),

$2p-5p=6$

$-3p=6$

$p=-6/3$

$p=-2$



Putting $p=-2$ in (1),

$q=5(-2)$

$q=-10$




$Hope\:you\:understand.$