Set up the system of equations:
[tex]8x + 5y = 30.75[/tex]
[tex]7x + 6y = 33[/tex]
We'll use elimination to solve this system of equations.
Take the coefficients for y in both problems. Multiply one of them by -1:
[tex]5 \times -1 = -5[/tex]
Since this coefficient is taken from the first problem, we'll multiply the entire second problem by this negative coefficient:
[tex](7x + 6y = 33) \times -5 = -35x - 30y = -165[/tex]
Take the coefficient for y in the second problem and multiply the entire first problem by that coefficient:
[tex](8x + 5y = 30.75) \times 6 = 48x + 30y = 184.50[/tex]
Your system should now look like this:
[tex]48x + 30y = 184.50[/tex]
[tex]-35x - 30y = -165[/tex]
Combine these two equations to cancel out y:
[tex]13x = 19.50[/tex]
Divide both sides by 5 to get x by itself:
[tex]x = 1.5[/tex]
A fairy soda costs $1.50.
Because we know the value of one of the variables, we can plug it into one of the equations:
[tex]8(1.5) + 5y = 30.75[/tex]
[tex]12 + 5y = 30.75[/tex]
Subtract 12 from both sides:
[tex]5y = 18.75[/tex]
Divide both sides by 5 to get y by itself:
[tex]y = 3.75[/tex]
A fairy hotdog costs $3.75.
