Tyler went to the supermarket to buy food for a food pantry. he has $36, and can carry up to 20 pounds of food in his backpack. pasta costs $1 for a 1-pound package. pasta sauce costs $3 for a 1.5 pound jar. let x = the number of packages of pasta and y = the number of jars of pasta sauce. identify each point as either a solution to the system or not a solution to the system of inequalities. (1, 12) (2, 10) (4, 5) (6, 10) (12, 8) (18, 6) .

Solutions: (2,10), (4,5)

Not solutions: (1,12), (6,10), (12,8), (18,6)

Step-by-step explanation:

Let x be the number of packages of pasta and y be the number of jars of pasta sauce. If pasta costs $1 for a 1-pound package, then x packages of pasta cost $x and weigh x pounds. If pasta sauce costs $3 for a 1.5 pound jar, then y jars cost $3y and weigh 1.5y pounds.

1. Tyler has $36, then

2. Tyler can carry up to 20 pounds of food in his backpack, then

You get the following system of inequalities:

Now substitute the coordinates of each point:

(1,12):

False, because first inequality doesn't hold.

(2,10):

True, both inequalities hold.

(4,5):

True, both inequalities hold.

(6,10):

False, because secondt inequality doesn't hold.

(12,8):

False, because second inequality doesn't hold.

(18,6):

False, because second inequality doesn't hold.