A group of students goes out to lunch. If two have burritos and five have tacos, the bill will be $19.50. If five burritos and two tacos, the bill will be $22.50. Find the price of a taco and the price of a burrito. (Can someone please help me and show the equation and steps to solve)

Tacos cost $2.50 each

Burritos cost $3.50 each

Step-by-step explanation:

Price variables:

  tacos:  t

  burritos:  b

Constraints:

  2b + 5t = 19.50

  5b + 2t = 22.50

2b + 5t = 19.50

2b  = 19.50 - 5t

b = 9.75 - 5/2t

5b + 2t = 22.50

5(9.75 - 5/2t) + 2t = 22.50

48.75 - 12.50t + 2t = 22.50

48.75 - 10.50t = 22.50

-10.50t = -26.25

t = 2.50

2b + 5t = 19.50

2b + 5(2.50) = 19.50

2b + 12.50 = 19.50

2b = 7

b = 3.50