[tex] 3x + 2y = 20 [/tex]
[tex] 8x + 4y = 45 [/tex]
[tex] where x = # of movies [/tex] and [tex] y = # of video games [/tex]
In order to solve this systems of equations problem, you need to use the elimination method.
You can multiply the top equation, [tex] 3x + 2y = 20 [/tex], by -2 in order to eliminate the [tex] y [/tex] values.
[tex] (3x + 2y = 20) *-2 [/tex] will turn into [tex] -6x - 4y = -40 [/tex]
From there, we can eliminate.
[tex] -6x - 4y = -40 [/tex]
[tex] 8x + 4y = 45 [/tex]
Since [tex] 4y [/tex] and [tex] -4y [/tex] are opposites in sign and equal in coefficients, we can remove them from our equations and add the rest of the terms together.
[tex] -6x - 4y = -40 [/tex]
[tex] 8x + 4y = 45 [/tex]
will turn into -->
[tex] 2x = 5 [/tex]
So, x = [tex] \frac{5}{2} [/tex], which means 1 movie costs $2.50. Then, we can solve for the video game price, [tex] y [/tex], by substituting our x back into one of the equations.
[tex] 3x + 2y = 20 [/tex]
[tex] 3*\frac{5}{2} + 2y = 20 [/tex]
[tex] y = \frac{25}{4} [/tex]
Each movie costs $2.50 and each video game costs $6.25.
