Question

find values of a and b for which the following system of equations has infinitely many solutions? 3x+4y=1
(a+b)x+2(a-b)y=5a-1 ​

Answer 1

Given: Two equations 3x + 4y = 1  and (a+b)x + 2(a-b)y = 5a - 1

To find: The values of a and b ?

Solution:

• Now we have given two equations:

               3x + 4y = 1  and (a+b)x + 2(a-b)y = 5a - 1

• The system has infinitely many solutions, so:

               a1/a2 = b1/b2 = c1/c2

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

• Comparing 1st and 2nd, we get:

               3 / a+b = 4 / 2(a-b)

               6(a-b) = 4(a+b)

               6a - 6b = 4a + 4b

               2a = 10b

               a = 5b

• Comparing 2nd and 3rd, we get:

               4 / 2(a-b) = 1 / 5a-1

               4(5a-1) = 2(a-b)

               20a - 4 = 2a - b

               18a = 4 - b

• Putting value of a in above equation, we get:

               18(5b) = 4 - b

               90b = 4 - b

               91b = 4

               b = 4/91

               a = 5(4/91)

               a = 20/91

Answer:

               So the value of a is 20/91 and b is 4/91.