the 2-digit positive integers problem

Each of x, y, and z is a 2-digit positive integer (in base ten), and:
1) 4x + y – 19z = 0
2) 2x + y – 14z = 0
Solve for x.
This problem (stated in terms of a, b, and c, and with base ten merely presumed), is on the web, among a set of tournament problems.
Here is the set of tournament problems (as a pdf file).
keywords: Mathematics, Number Theory, challenge