The total of two numbers is 28. four times the smaller number is 7 more than three times the larger number. smaller number=? larger number=?

Let the two numbers be represented by x and y, x being smallest.
.. x + y = 28 . . . . . . the total is 28
.. 4x = 7 + 3y . . . . . 4 times the smallest is 7 more than 3 times the largest

Subtract the second equation from 4 times the first to eliminate x.
.. 4(x +y) -(4x) = 4(28) -(7+3y)
.. 4y = 105 -3y . . . . . . . . . . . . . . simplify. Notice x is gone.
.. 7y = 105 . . . . . . . . . . . . . . . . . add 3y
.. y = 15 . . . . . . . . . . . . . . . . . . . divide by 7

.. x = 28 -y = 13

Smaller number = 13
Larger number = 15