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
