Cost of games and puzzles (system of equations)

Two games and five puzzles cost $33.25 altogether. Three games and two puzzles cost $32.00. If every
game costs the same amount, and every puzzle costs the same amount, what is the cost of each puzzle?

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x = cost of 1 game
y = cost of 1 puzzle

2x + 5y = 33.25   {two games and five puzzles cost $33.25}
3x + 2y = 32  {three games and two puzzles cost 32}

-3(2x + 5y = 33.25)  {multiplied top equation by -3}
2(3x + 2y = 32)  {multiplied bottom equation by 2}

-6x - 15y = -99.75  {new top equation}
6x + 4y = 64   {new bottom equation}
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11y = -35.75  {added the two new equations, eliminating the x}
y = 3.25  {divided each side by 11}

3x + 2y = 32  {original bottom equation}
3x + 2(3.25) = 32   {substituted 3.25, in for y, into bottom original equation}
3x + 6.5 = 32  {multiplied 2 by 3.25}
3x = 25.5   {subtracted 6.5 from each side}
x = 8.5  {divided each side by 3}

cost of each game is $3.25
cost of each puzzle is $8.50

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