Answer:
[tex]m=10\\v=\frac{10}{3}[/tex]
Step-by-step explanation:
2 movies and 6 video games for $40. [tex]2m+6v=40[/tex] 5 movies and 3 video games for $25. [tex]5m+3v=25[/tex]
We set up systems of equations.
[tex]2m+6v=40[/tex]
[tex]5m+3v=25[/tex]
[tex]5(2m+6v=40)\\2(5m+3v=25)\\[/tex] <-- This step is done so we can make the numbers before the [tex]m[/tex] the same.
[tex]10m+30v=200\\10m+6v=50\\[/tex]<-- Notice now how the numbers before the [tex]m[/tex] are the same.
Now, since the numbers before the [tex]m[/tex] are the same, we subtract to get rid of them.
[tex]24m=150[/tex]
We now know that [tex]m=10[/tex]
Replace 10 as [tex]m[/tex] in the first eqation to find [tex]v[/tex]: [tex]2(10)+6v=40[/tex]
Solve
[tex]20+6v=40\\6v=20\\v=\frac{20}{6} = \frac{10}{3}[/tex]
Therefore [tex]m=10\\v=\frac{10}{3}[/tex]
