Write the relation between a, b, c, p, q and r for which the pair of linear equations ax+by+c = - Maths - Pair of Linear Equations in Two Variables

Question

Write the relation between a, b, c, p, q and r for which the pair
of linear equations ax+by+c = 0 and px+qy+r = 0 will represent
parallel lines

Mohammed Javed · Accepted Answer

Dear Student

Givenax +by + c = 0     
(i)px  + qy +r = 0     
(ii)Comparing equation (i) and (ii) with a1x +b1y + c1 = 0 and a2x +b2y + c2 = 0a1 = a   ;   b1 = b    ;   c1 = ca2 = p    ;   b2 = q   ;   c2 = rWe know that for a pair of linear equation to be parallela1a2 = b1b2 ≠ c1c2Thereforeap = bq ≠ crRegards

Write the relation between a, b, c, p, q and r for which the pair of linear equations ax+by+c = 0 and px+qy+r = 0 will represent parallel lines.