Diego is thinking of two positive numbers, if we triple the first number and double the second number the sum is 34. Diego then says, "if we take half of the first of the first number and double the second number, the sum is 34. What are Diego’s two numbers?

1st number: 0

2nd number: 17

Step-by-step explanation:

3x+2y=34 x is the first number, y is the second.

1/2x+2y=34 multiply each number by two to get rid of the integer by the variable x.

x+4y=68 solve for x.

x=68-4y add this into the first equation to solve for variable y.

3(68-4y)+2y=34 solve for y.

204-10y=34

-10y= -170

y=17

now to solve for x

x= 68-4(17)

x= 0