what is the second part to this question

Question

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. [answer1]

Find two possible pairs of numbers Diego could be thinking of (write as ordered pair). [answer3]

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. [answer2]

What are Diego’s two numbers?

Answer 1

[answer 1] 3x+2y=34

[answer 3] (10,2) and (4,11) will work for the equation

[answer 2] x/2+2y=14

What are Diego's two number given the two equations?

A system of 2 equatons can be solved in several ways. Let's use substitution.

Take the second equation and solve for x:

x = 2(14-2y) = 28-4y

and substitute into x in the first equation

3(28-4y) +2y = 34

and solve for y

84-12y + 2y = 34 -> -10y =-84-34 = -50 -> y = -50/-10 = 5

Substituting y = 5 into the first equation: 3x+2(5)= 34 -> 3x = 34-10 = 24 -> x = 24/3 = 8

So Diego's two numbers are (8,5)

Checking: 3(8) + 2(5) = 24 + 10 = 34, 8/2 + 2(5) = 4 + 10 = 14 √