Understanding and generating non-linear equations in two or more variables

Which equation represents the total earned from ticket sales.

• $x+y=250$

•  $15x\ +\ 10y\ =\ 3000$ 

•  $250\ +\ 15x\ =\ 3000\ +10y$ 

•  $15x\ +\ 10y\ =250$ 

• $x+y=3000$

Payton took his 2 best friends to the movie theatre and paid for their food.  The cost of 3 large soda’s, 4 hot dogs, and 2 bags of sour patch kids cost $20.50.  The cost of 2 soda’s and 4 hot dogs is $12.00.  The cost of 3 hot dogs and 2 bags of sour patch kids is $8.75.  If x represents sodas y represents hot dogs, and z represents bags of sour patch kids, which system of equations can be used can be used to determine the sale price of the sodas, hot dogs, and bags of sour patch kids?

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold? Let S represent the number of student tickets, and let A represent the number of adult tickets.

• S + A = 530 3S + 4A = 1740

• S + A = 530 4S + 3A = 1740

• S + A = 1740 3S + 4A = 530

• S + A = 1740 4S + 3A = 530

The sum of two numbers is 6 and their difference is 2. Which of the 

       following systems of linear equations in two variables illustrate the 

       problem?

• x + y = 6

  x - y = 2

• x + y = 6

  x + y = 2

• x - y = 6

  x + y = 2

• x - y = 6

  x - y = 2

Robert is thinking of two numbers. Their sum is -10 and their difference is -2. Which system of equations represents this situation?

• x - y = -10 and x + y = -2

• x = -2 and y = -10

• x + y = -10 and x - y = -2

• x + y = -2 and x - y = -10

What is the value for B

You have $18 to spend on Uber Eats credits and hats for Among us. Uber Eats credits are $1 each and hats for Among Us cost $2 each.

Let x = # of Uber Eats credits

Ley y = # of hats for Among Us

What equation should you use for this word problem?

• y+18x=2

• 2x+y=18

• x+2y=18

• 18x+y=2

Which equation matches this scenario?

I bought 5 cakes and 4 sodas for $23

• 5c + 4s = 23

• 5c x 4s = 23

• 5s + 4c = 23

• 5s x 4c = 23

There are a total of 52 students on the soccer team and the field hockey team. The field hockey team has 12 more students than the soccer team. Write a system of linear equations that fits this situation.

• $x+y=52$
  $y=x+12$
  

• $x+y=52$
  $x=y+12$
  

• $x+12=52$
  $x+y=52$
  

The store at which Andy usually shops is having a sale. Roast beef costs $4 a pound and shrimp costs $10 a pound. Write an equation to describe different possible combinations of r Roast beef and s shrimp that he can buy for $100.

• $4r+10s=100$

• $4s+10r=100$

• $4r+10=100$

• $4r+10r=100$