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For what values of m and n the following system of linear equations has infinitelymany solutions.3x + 4y 12(m + n) x 2 (m -n) y 5m-1 |
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Answer» Answer: m = 5 & n = 1 Step-by-step explanation: Find the value of m and n 3x+4y=12(m+n)x+2(m-n)Y=5m-1 complete question is find values of m&n for infinite solution to have infinite solutions both equation should be same (m+n)x + 2(m-n)y = 5m-1 should be equivalent to 3x + 4y = 12 => k*3x + k*4y = k*12 where k is any variable => (m+n)/3 = 2(m-n)/4 = (5m-1)/12 = k Multiplying each with 12 => 4m + 4n = 6m - 6n = 5m -1 = 12k taking 1st 2 equations 4m + 4n = 6m - 6n => 10n = 2m => m = 5n - eq A taking 1st & 3rd 4m + 4n = 5m-1 => m = 4n + 1 - eq B equating value of m from eq A & eq B 5n = 4n + 1 => n = 1 putting value of n in eq A m = 5*1 = 5 Hence value of m = 5 & n = 1 |
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