Let m and v represent the cost of a movie rental and a video rental.
Then 3m + 5v = $38 and 12m + 2v = $53. Solve this system of linear equations:
3m + 5v = $38
12m + 2v = $53
Let's eliminate m. Mult. the first eqn by -4, obtaining -12m - 20v = $152.
Now add this result to the 2nd equation:
-12m - 20v = -$152
12m + 2v = $53
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-18v = -$99
Solving this for v, the cost of renting one video, is v = $99/18, or $5.50.
Now sub $5.50 for v in 3m + 5v = $38:
3m + $27.50 = $38. Then m, the cost of renting one movie, is $10.50.