Solve the following pairs of equations 2a 3b 17 3a 2b 6S

Solve the following pairs of equations:

2a + 3b = 17

3a - 2b = 6

Solution

The given equations are 2a + 3b = 17...(1) and 3a - 2b = 6. On multiplying both the sides of the 1st equation by 2 and the 2nd equation by 3, we have 4a + 6b = 34...(3) and 9a - 6b = 18...(4).

Now, on addiing the 3rd and the 4th equations, we have 4a + 6b + 9a - 6b = 34 + 18 or, 13a = 52. Therefore, a = 52/13 = 4. Then , on substituting a = 4 in the 1st equation, we have 2 * 4 + 3b = 17 or, 3b = 17 - 8 = 9 so that b = 9/3 = 3. Thus, the answer is a = 4 and b = 3. We can verify the result by substituting these values of a and b in the 2nd equation.