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.

Answer 1

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