Solve the following systems of simultaneous linear equations by the elimination method
px + qy = p - q
qx - py = p + q

Question

Solve the following systems of simultaneous linear equations by the elimination method px + qy = p - q qx - py = p + q

KnowledgeBoat · Accepted Answer

Given, px + qy = p - q .......(i) qx - py = p + q .......(ii) Multiplying eq. (i) by q and eq. (ii) by p we get, pqx + q²y = pq - q² .......(iii) pqx - p²y = p² + pq .......(iv) Subtracting eq. (iv) from (iii) we get, ⇒ pqx + q²y - (pqx - p²y) = pq - q² - (p² + pq) ⇒ pqx - pqx + q²y + p²y = pq - pq - q² - p² ⇒ q²y + p²y = -q² - p² ⇒ y(q² + p²) = -(q² + p²) ⇒ y = = -1. Substituting value of y in eq. (i) we get, ⇒ px + q(-1) = p - q ⇒ px - q = p - q ⇒ px = p - q + q ⇒ px = p ⇒ x = 1. Hence, x = 1 and y = -1.

Mathematics

Solve the following systems of simultaneous linear equations by the elimination method
px + qy = p - q
qx - py = p + q

Linear Equations

Related Questions

Solve 2x + y = 23, 4x - y = 19. Hence, find the values of x - 3y and 5y - 2x.

Mathematics

Solve the following systems of simultaneous linear equations by the elimination methodpx + qy = p - qqx - py = p + q

Linear Equations

Related Questions

Solve 2x + y = 23, 4x - y = 19. Hence, find the values of x - 3y and 5y - 2x.

Solve the following systems of simultaneous linear equations by the elimination method
px + qy = p - q
qx - py = p + q