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11: For what value of p the pair of linear equations(+ 2)-p+ y- 32p-and 2x-3y - 7has a unique solution. |
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Answer» The Given pair of linear equation is :(p+ 2)x - (2p + 1)y = 3(2p -1) ……….(1)2x- 3y = 7 ………….(2) On comparing with General form of a pair of linear equations in two variables x & y is:a1x + b1y + c1 = 0and a2x + b2y + c2= 0 a1= (p+2) , b1= - (2p+1), c= - (3(2p -1))a2= 2 , b2= -3 , c= -7 a1/a2= (p+2) /2 , b1/b2= -(2p+1)/-3 Given: A pair of linear equations has a Unique solution, ifa1/a2 ≠ b1/b2 (p+2) /2 ≠ -(2p+1)/-3-3(p+2) ≠ 2(-2p-1)-3p -6 ≠ -4p -2-3p + 4p ≠ - 2 +6p ≠ 4Hence, the value of p ≠ 4 |
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