Answer:
one hamburger costs 3 dollars
one hot dog costs 2.50 dollars
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Work Shown:
x = cost for one hamburger
y = cost for one hot dog
3x = cost for 3 hamburgers
4y = cost for 4 hot dogs
3x+4y = total cost for 3 hamburgers, 4 hot dogs
3x+4y = 19
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5x = cost for 5 hamburgers
2y = cost for 2 hot dogs
5x+2y = total cost for 5 hamburgers, 2 hot dogs
5x+2y = 20
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The equations we have set up are
3x+4y = 19
5x+2y = 20
If we multiply everything in the second equation by 2, then we have 5x+2y = 20 turn into 10x+4y = 40
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So we have this equivalent system
3x+4y = 19
10x+4y = 40
Subtract straight down to get -7x = -21 which solves to x = 3.
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use the value of x to find y
3x+4y = 19
3*3+4y = 19
9+4y = 19
4y = 19-9
4y = 10
y = 10/4
y = 2.50