Question 1045376
x = cost of one dozen roses.
y = cost of one dozen carnations.


20x + 34y = 504
15x + 17y = 327


you need to solve these 2 equations simultaneously.


if you multiply 17 by 2, you get 34.
therefore, the coefficient of y is a good candidate.


multiply both sides of the second equation by 2 and leave the first equation as is to get:


20x + 34y = 504
30x + 34y = 654


subtract the second equation from the first to get:


-10x = -150


solve for x to get x = 15.


replace x with 15 in either of the original equations and solve for y.


you will get y = 6


price of a dozen roses is 15 and price of a dozen carnations is 6.


note that i could also have done the following and gotten the same result.


start with:


20x + 34y = 504
15x + 17y = 327


multiply both sides of the second equation by -2 and leave the first equation as is to get:


20x + 34y = 504
-30x - 34y = -654


add the 2 equations together to get:


-10x = -150


solve for x to get x = 150.


if i multiplied by plus 2, then i subtracted one equation from the other to eliminate the y variable.


if i multiplied by minus 2, then i added one equation to the other to eliminate the y variable.


both methods work.


choose the one you feel more comfortable with.