Answer: the cost of a DVD is $8 and the cost of a video game is $33
Step-by-step explanation:
Let x represent the cost of a video game.
Let y represent the cost of a DVD.
2 video games and 3 DVDs cost $90.00. This is expressed as
2x + 3y = 90 - - - - - - - - - - - 1
1 video game and 2 DVDs cost $49.00. This is expressed as
x + 2y = 49 - - - - - - - - - - - 2
Multiplying equation 1 by 1 and equation 2 by 2, it becomes
2x + 3y = 90 - - - - - - - - - - - -3
2x + 4y = 98 - - - - - - - - - - - - 4
Subtracting equation 4 from equation 3, it becomes
3y - 4y = 90 - 98
- y = - 8
y = 8
Substituting y = 8 into equation 2, it becomes
x + 2 × 8 = 49
x + 16 = 49
x = 49 - 16
x = 33
