macaroni has 3 grams of protein per serving and 2 gram of carbohydrates per serving.
macaroni has 16 grams of carbohydrates per serving and broccoli has 4 grams of carbohydrates per serving.
if you want a total of 37 grams of protetin and 164 grams of carbohydrates, ten your equations are:
3x + 2y = 37
16x + 4y = 164
the first equation says 3 grams of protein per serving times the number of servings of macaroni plus 2 grams of protein per serving times the number of servings of broccoli equals a total of 37 grams of protein.
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the second equation says 16 grams of carbohydrates per serving times the number of servings of macaroni plus 4 grams of carbohydrates per serving times the number of servings of broccoli equals a total of 164 grams of carbohydrates.
you need to solve these equations simultaneously so the same number of servings of macaroni and broccoli apply to both equations.
if you graphed these equations, your solution would be the intersection of the graphs of both equations, as shown below:
from the graph, you can see that the intersection of the two lines is the point (9,5).
that means the value of x = 9 and y = 5.
that means 9 servings of macaroni and 5 servings of broccoli is the solution.
3 * 9 + 2 * 5 = 27 + 10 = 37 grams of protein.
16 * 9 + 4 * 5 = 144 + 20 = 164 grams of carbohydrates.
the solution looks good.
to solve this problem algebraically, you would do the following:
start with:
3x + 2y = 37
16x + 4y = 164
multiply the first equation by 2 and leave the second equation as is to get:
6x + 4y = 74
16x + 4y = 164
subtract the first equation from the second to get:
10x = 90
divide both sides of this equation by 10 t9o get x = 9.
replace x with 9 in either original equaiton (i used the first), to get:
3*9 + 2y = 37 which becomes 27 + 2y = 37.
subtract 27 from both sides to get 2y = 10
solve for y to get y = 5.
your solution is x = 9 and y = 5.
since this agrees with the graphical solution, there is no need for further confirmation that the solution is valid.
your solution is you need 9 servings of macaroni and 5 servings of broccoli.