I need help, please i dont understand. Its algebra 2

Question

A total of $22,000 was invested, part of at 10% and part at 12%. The total yeild was $2900. How much was invested at each rate

Answer 1

Let: 

X=amt. invested at 10%

Y=amt. invested at 12%

 We have 2 unknowns, therefore we need 2 equations to solve the problem. We know that our initial total investment is $22,000 and that our total yield is $2900. Therefore:

    X + Y = 22,000

    0.10X + 0.12Y = 2900

By using the substitution method:

    Y = 22,000 - X (from the first equation)

Substituting this value of X into the 2nd equation we can solve for Y:

    0.10X + 0.12(22,000-X) = 2900

    0.10X +2640 - 0.12X = 2900

    -0.02X = 260

    X = 260/-0.02

     X=-13,000

Putting this value of X into the 1st equation we can solve for Y:

     Y= 22,000 - X

     Y = 22,000 -(-13,000)

     Y = 35,000

Therefore the answer is:

     $35,000 is invested at 12% and -$13,000 is invested at 10%.