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Question
Find the values of 'a' and 'b' for which the system of linear equations 3x + 4y = 12, (a + b)x + 2(a – b)y = 24 has infinite number of solutions.
Solution
Given that,
3x + 4y = 12
(a + b)x + 2(a – b)y = 24
For infinite number of solutions,
`\implies 3/("a" + "b") = 4/(2("a" - "b")) = 12/24`
`\implies 3/(("a" + "b")) = 1/2`
`\implies` a + b = 6 ...(i)
Also, `2/(("a" - "b")) = 1/2`
`\implies` a – b = 4 ...(ii)
From equations (i) and (ii),
`\implies` a = 5, b = 1
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