Question

Find the value of a and b for each of the following system of linear equations has a infinite number of solutions; 2x+3y=7;(a+b+1)x-+(a+2bb+2)y=4(a+b)+1

Answer 1

2x + 3y = 7 and (a + b)x + (a + 2b + 2)y = 4(a + b)+1

for infinite solution ,
2/(a + b + 1) = 3/(a + 2b + 2) = 7/(4a + 4b + 1)

2/(a + b + 1) = 7/(4a + 4b + 1)
2(4a + 4b + 1) = 7(a + b + 1)
8a + 8b + 2 = 7a + 7b + 7
a - b = 5 --------(1)

3/(a + 2b + 2) = 7/(4a + 4b+ 1)
3(4a + 4b + 1) = 7(a + 2b + 1)
12a + 12b + 3 = 7a + 7b + 7
5a + 5b = 4 -------(2)

now, from equations (1) and (2)
5a + 5a = 25 + 4
a = 2.9 , b = -5 + 2.9 = -2.1