Help with word problem (algebra)

The school that Molly goes to is selling tickets to a spring musical. On the first day of ticket sales the school sold 4 senior citizen tickets and 1 student ticket for a total of $21. The school took in $84 on the second day by selling 4 senior citizen tickets and 8 student tickets. What is the price each of one senior citizen ticket and one student ticket?

Write and solve a system by elimination. Show work please. Thank you!

s is senior, r is regular student.
4s+r=21
4s+8r=84
Subtract one system from the other.
-7r=-63
solve the equation.
r=9
substitute r=9 into the original equation
4s+9=21
Solve the equation
s=3
A senior ticket costs 3 dollars, and a student ticket costs 9 dollars.
Feel free to check my work.

Call the price at which a senior ticket sells x, and the price for a student ticket y.
Then the first day, 4 senior tickets and 1 student ticket for $21, so 4x + y = 21
On the second day, 4 senior tickets and 8 student tickets went for $84. 4x + 8y = 84
Then, solve the equations:
4x + 8y = 84
- 4x + 1y = 21
--------------------
7y = 63 --> y = 9
Then plug y back into the first equation (4x + y = 21)
4x + 9 = 21 --> 4x = 12, therefore x=3. So each senior ticket costs $3 and every student ticket is $9. So, the price of one of each ticket would be $12.

Keep it real.