Gabriellas school is selling tickets to a fall musical. On the dirst day of ticket sales the school sold 10 senior citizen tickets and 14 student tickets for a total of $212. Tje school took in$232 on the second day by selling 12 senior citizen tickets and 14 student tickets. What is the price each of one senior citizen tickets and one student ticket?

A senior ticket costs $10, while a student ticket costs $8. You can solve this system of equations by the elimination method.

We can use x as the variable for the senior tickets, and y as the variable for the student tickets and represent it with these equations:
10x+12y=212 and 12x+14y=232

Next, multiply each entire equation by a variable so they can eliminate each other. I used 12 and -10 here so it would be 120x-120x to eliminate that variable.
12(10x+14y=212) and -10(12x+14y=232)

Our new equations are:
(120x +168y= 2544) and (-120x-140y=-2320)

You can then subtract one of the equations from the other leaving you with 28y=224 and solve it for y to get 8.
So the price of a student ticket is 8.

Pick any of the original equations and by replacing y with 8, you can solve to find x. (X is the variable we assigned for senior tickets)
10x+14(8)=212
10x+112=212
10x=212-112
10x= 100
1x=10