Question

5p-3r=1

Answer 1

To answer, multiply the first equation by 2. Then, add the equations,
                                10p - 6r = 2
                         +       8p + 6r = 4
The resulting sum would be 18p = 6. The value of p from the equation is p = 1/3. Substitute this value to either of the equation,
                                 10(1/3) - 6r = 2    ; r = 2/9
Thus, the answer is letter C. 

Answer 2

If you would like to solve the system of equations, you can do this using the following steps:

5p - 3r = 1     /*2
8p + 6r = 4
__________
10p - 6r = 2
8p + 6r = 4
__________
10p - 6r + 8p + 6r = 2 + 4
18p = 6
p = 6/18
p = 1/3

5p - 3r = 1
5 * 1/3 - 3r = 1
5/3 - 3r = 1
5/3 - 1 = 3r
5/3 - 3/3 = 3r
2/3 = 3r
r = 2/9

(p, r) = (1/3, 2/9)

The correct result would be (1/3, 2/9).