Kat has 19 coins, all quarters and dimes, that are worth a total of $4. the system of equations that can be used to find the number of quarters, q, and the number of dimes, d, she has is shown. q d=19 0.25q 0.1d=4

Let q be the number of 25 cent coins.
Let d be the number of 10 cent coins.

0.25q+0.10d= 4...(1)
q+d= 19..(2)

(2)-> q+d=19
      q+d-d= 19-d
             q= 19-d...(2a)

(2a)->(1)  0.25q+0.10d=4
       0.25(19-d)+0.10d= 4
      4.75-0.25d+0.10d= 4
                        -0.15d=4-4.75
               -0.15d/-0.15= -0.75/-0.15
                                d= 5...(3)

(3)->(2)    q+d=19
                q+5=19
                    q=19-5
                    q= 14
There are 14 quarters and 5 coins.