Diego is thinking of two positive numbers. He says, “If we triple the first number and double the second number, the sum is 34.”

Write an equation that represents this clue. Then, find two possible pairs of numbers Diego could be thinking of.
Diego then says, “If we take half of the first number and double the second, the sum is 14.”

Write an equation that could represent this description.

What are Diego’s two numbers? Explain or show how you know. A coordinate plane is given here, in case helpful.