Let's try to solve for x and see if we can find a solution for the given equation:
5x + 17 = 4(3x - 1)
Distribute the product on the right side
5x + 17 = 12x - 4
Subtract 5x on both sides
5x - 5x + 17 = 12x - 5x - 4
Conbine like terms
17 = 7x - 4
Add 4 on both sides
21 = 7x
Divide both sides by 7
x = 21/7 = 3
x = 3
As you can see, the given system has one solution
