Home
Class 10
MATHS
Solve the following system of equations ...

Solve the following system of equations . `x/p+y/q=1`, `p(x-p)-q(y+q)=2p^2 + q^2`

Text Solution

Verified by Experts

`x/p+y/q = 1`
`=>qx+py = pq->(1)`
`p(x-p)-q(y+q) = 2p^2+q^2`
`=>px-p^2-qy+q^2 = 2p^2+q^2`
`=>px-qy = 3p^2+2q^2->(2)`
Multiplying (1) by `q` and (2) by `p` and adding them,
`q^2x+pqy+p^2x-pqy = pq^2+3p^3+2pq^2`
`(p^2+q^2)x +3p(p^2+q^2)`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

Solve the following system of equations.(x)/(p)+(y)/(q)=1p(x-p)-q(y+q)=2p^(2)+q^(2)

Solve the following pair of linear equations: (i) p x+q y=p q ;" "q x p y=p+q (ii) a x+b y=c ;" "b x+a y=1+c (iii) x/a-y/b=0 ; a x+b y=a^2+b^2 (iv) (a-b)x+(a+b)y=a^2-2a b-b^2; (a+b)(x+y)=a^2+b^2 (v) 152 x 378 y= 74 ;" " 378

Solve the following equation for x: 9x^(2)-9(p+q)x+(2p^(2)+5pq+2q^(2))=0

If p and q are the roots of the equation x^2-p x+q=0 , then

If each pair ofthe following three equations x: x^(2)+p_(1)x+q_(1)=0.x^(2)+p_(2)x+q_(2)=0x^(2)+p_(3)x+q_(3)=0, has exactly one root common, prove that (p_(1)+p_(2)+p_(3))^(2)=4(p_(1)p_(2)+p_(2)p_(3)+p_(3)p_(1)-q_(1)-q_(2)-q_(3)]

Find the values of p and q for which the following system of equations has infinite number of solutions: 2x+3y=7,\ \ \ \ (p+q)x+(2p-q)y=21

Find the values of p and q for which the following system of equations has infinite number of solutions: 2x+3y=7,\ \ \ \ (p+q)x+(2p-q)y=21

Find the values of p and q for which the following system of equations has infinite number of solutions: 2x+3y=7,quad (p+q)x+(2p-q)y=21

If p and q are the roots of the equation x^(2)+p x+q=0 then