Select Board & Class

Login

Pair Of Linear Equations In Two Variables

Question 7:

Solve the following pair of linear equations.

(i) px + qy = pq

qx py = p + q

(ii) ax + by = c

bx + ay = 1 + c

(iii)

ax + by = a2 + b2

(iv) (ab) x + (a + b) y = a2− 2abb2

(a + b) (x + y) = a2 + b2

(v) 152x − 378y = − 74

− 378x + 152y = − 604

Answer:

(i)px + qy = pq … (1)

qx py = p + q … (2)

Multiplying equation (1) by p and equation (2) by q, we obtain

p2x + pqy = p2pq … (3)

q2xpqy = pq + q2 … (4)

Adding equations (3) and (4), we obtain

p2x + q2 x = p2 + q2

(p2 + q2) x = p2 + q2

From equation (1), we obtain

p (1) + qy = pq

qy = − q

y = − 1

(ii)ax + by = c … (1)

bx + ay = 1 + c … (2)

Multiplying equation (1) by a and equation (2) by b, we obtain

a2x + aby = ac … (3)

b2x + aby = b + bc … (4)

Subtracting equation (4) from equation (3),

(a2b2) x = acbcb

From equation (1), we obtain

ax + by = c

(iii)

Or, bx − ...

To view the solution to this question please

What are you looking for?

Syllabus