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which values of P and Q, will the following pair of linear equations have infinitely many solutions for4 X + 5 Y = 2 ,( 2 p+ 7q) X + (p+8q) Y =2q-p+1 |
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Answer» Answer: p = -1 and q = 2 Step-by-step explanation: 4x + 5Y - 2 = 0 (2p+7Q)x + (p+8q)y - (2q-p+1) = 0 given eq. is infinite solution so, a1/a2 = b1/b2 = c1/c2 4/(2p+7q) = 5/(p+7q) = -2/[-(2q-p+1)] on COMPARING a1/a2 = c1/c2 4/(2p + 7q) = 2/(2q - p + 1) 4(2q - p +1) = 2(2p + 7q) 8q - 4p + 4 = 4p + 14q 4p + 14q - 8q + 4p = 4 8p + 6q = 4 --------------------(1)
now, b1/b2 = c1/c2 5/(p + 7q) = 2/(2q - p + 1) 5(2q - p + 1) = 2(p + 8q) 10q - 5q + 5 = 2p + 16q 2p + 16q - 10q + 5p = 5 7p + 6q = 5 ---------------------(2) on subtract eq. 1 and 2 8p + 6q = 4 7p + 6q = 5 - - - .................................... p = -1PUT the value of p in eq. 1 8p + 6q = 4 8(-1) + 6q = 4 -8 + 6q = 4 6q = 4 + 8 6q = 12 q = 12/6 q = 2
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