Multiply the first equation by 8 and the second equation by 7.

8(7p + 5q) = 8(2)

7(8p - 9q) = 7(17)

Subtract the result of the second multiplication from the results of the first.

(56p + 40q) - (56p - 63q) = 16 - 119

103q = -103 (notice that p is eliminated)

q = -1

Substitute this result into the first equation.

7p + 5(-1) = 2

7p = 7

p = 1

8(7p + 5q) = 8(2)

**56p + 40q = 16**7(8p - 9q) = 7(17)

**56p - 63q = 119**Subtract the result of the second multiplication from the results of the first.

(56p + 40q) - (56p - 63q) = 16 - 119

103q = -103 (notice that p is eliminated)

q = -1

Substitute this result into the first equation.

7p + 5(-1) = 2

7p = 7

p = 1

**The solution is (p, q) = (1, -1).**