Question

$px + qy = p - q \: \: \: \: \: and \: \: qx - py = p + q$
Solve this question by using only elimination method...........

Answer 1

Given equations are :

$px + qy = p - q \: \: \: \: \: \: \: \: \: \: \: \: (1)$

$qx - py = p + q \: \: \: \: \: \: \: \: \: \: \: (2)$

Multiply (1) by q and (2) by p

$q(px + qy) = q(p - q) \\ pqx \: + {q}^{2} y = pq - {q}^{2} \: \: \: \: \: \: \: \: (3)$

$p(qx - py) = p(p + q) \\ pqx - {p}^{2} y = {p}^{2} + pq \: \: \: \: \: \: \: \: \: \: (4)$

By applying Elimination Methd in equations (3) and (4)

$pqx + {q}^{2} y = pq - {q}^{2}$

$pqx - {p}^{2} y = pq + {p}^{2}$

- + - -

_________________________

${q}^{2} y+ {p}^{2} y = - {q}^{2} - {p}^{2}$

$y( {q}^{2} + {p}^{2} ) = - 1( {q}^{2} + {p}^{2} )$

$y = - 1$

__________________________

Put y = -1 in eq (1)

$px + q( - 1) = p - ( - 1)$

$px = p \\ x = 1$

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Answer 2

QUESTION -

$\tt px + qy = p - q \: \: \: \: \: and \: \: qx - py = p + q$

Solve this question by using only elimination method

ANSWER -

x = 1 and y = -1

STEP BY STEP EXPLANATION -

Multiplying p to equation (1) and q to equation (2), we get

➜ p²x + pqy = p² − pq ………… (iii)

➜ q²x − pqy = pq + q² ………… (iv)

Adding equation (iii) and equation (iv),we get

➜ p²x + q² x = p² + q²

➜ (p² + q² ) x = p² + q²

➜ x = (p² + q²)/ p² + q² = 1

From equation (i), we get

➜ p(1) + qy = p – q

➜ qy = p-q-p

➜ qy = -q

➜ y = -1

★ hence , x = 1 and y = -1