At a local basketball game all tickets are the same price and all souvenirs are the same price Mr. Smith put two tickets to this basketball game and one souvenir for a total of $17.25 Mrs. Lockhart bought five tickets the same game and to souvenirs for a total of $42 how much was your ticket to this game?

the cost of a ticket to the game is $7.5

Step-by-step explanation:

Let x represent the price of each ticket.

Let y represent the price of each souvenir.

Mr. Smith put two tickets to this basketball game and one souvenir for a total of $17.25. This is expressed as

2x + y = 17.25- - - - - - - - - - -1

Mrs. Lockhart bought five tickets for the same game and 2 souvenirs for a total of $42

This is expressed as

5x + 2y = 42- - - - - - - - - - -2

Multiplying equation 1 by 2 and equation 2 by 1. It becomes

4x + 2y = 34.5

5x + 2y = 42

Subtracting, it becomes

- x = - 7.5

x = 7.5

Substituting x = 7.5 into equation 1, it becomes

2 × 7.5 + y = 17.25

15 + y = 17.25

y = 17.25 - 15

y = 2.25