The two equations are
[tex]x + y = 7[/tex]
and
[tex]4x + 2.5y = 22[/tex]
the first equation can be solved for x to be
[tex]x = 7 - y[/tex]
next you can substitute x in the second equation
[tex]4(7 - y) + 2.5y = 22[/tex]
Distribute 4 to everything in the parentheses
[tex]28 - 4y + 2.5y = 22[/tex]
combine like terms:
[tex]28 - 1.5y = 22[/tex]
subtract 28 from both sides of the equation
[tex] - 1.5y = - 6[/tex]
divide both sides by -1.5
[tex]y = 4[/tex]
plug this in to the original equation of x+y=7
[tex]x + 4 = 7[/tex]
subtract 4 from both sides.
[tex]x = 3[/tex]
Final Answer: they bought 3 adult tickets and 4 student tickets
Hope this helps!
