Use the prices: adult tickets cost 7 dollars and student tickets cost 3 dollars. How can you write an equation for the total of 1,040 dollars using your variables?

You should now have two equations. Try to eliminate one variable: notice that one equation already has $a+s$. How could you multiply it so the $s$ terms in both equations match and can be subtracted?

Let $x$ represent the number of adult tickets and $y$ the number of student tickets. In Desmos, type the two equations in slope–intercept form:

• y = 200 - x (from $x+y=200$)
• y = (1040 - 7x)/3 (from $7x+3y=1040$).

Zoom or adjust the visible window until you can clearly see where the two lines cross. Click or tap on the intersection point. The $x$-coordinate of this point is the number of adult tickets sold, and the $y$-coordinate is the number of student tickets sold.

Let $a$ be the number of adult tickets and $s$ be the number of student tickets.

• Total tickets: $a+s=200$.
• Total money: each adult ticket is 7 dollars and each student ticket is 3 dollars, so

You now have a system of two equations in two variables.

Start with the system:

Multiply the first equation by 3 so the $s$-terms match:

Now subtract this new equation from the money equation:

This gives a single equation with only $a$.

From the previous step you have

Divide both sides by 4:

This fraction is the number of adult tickets sold.

Compute the value:

So 110 adult tickets were sold. As a quick check, that means $s=200-110=90$ student tickets. The total money is

which matches the fundraiser total, confirming that 110 is correct.