**Q) Solve the following pair of linear equations:px + qy = p – qqx – py = p + q**

**Ans: **

Given the equations:

Solve the following pair of linear equations:

px + qy = p – q …………. (i)

qx – py = p + q ………….. (ii)

Let’s multiply equation (i) with p and equation (ii) with q and we get:

p^{2} x + pq y = p^{2} – pq ^{ }

q^{2} x – pq y = pq + q^{2}

Let’s add these 2 equations:

p^{2} x + q^{2} x = p^{2} + q^{2}

∴ x (p^{2} + q^{2} ) = p^{2} + q^{2}

**∴ x = 1**

Let’s put x = 1 in equation (i), we get:

p (1) + qy = p – q

∴ qy = – q

**∴ y = – 1 **

**Therefore, x = 1 and y = – 1 **

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