Respuesta :
Given
Let's represent movies with M
Let's represent video with V
[tex]\begin{gathered} 8m+3v=43\ldots\text{Equation 1} \\ 2m+5v=32\ldots\text{Equation 2} \end{gathered}[/tex]Solution
Using substitution method
I will solve your system by substitution.
[tex]\begin{gathered} 8m+3v=43\ldots\text{Equation 1} \\ \text{Make M the subject of the formula} \\ 8m=43-3v \\ \text{Divide both sides by 8} \\ m=\frac{43-3v}{8}\ldots\text{Equation 3} \end{gathered}[/tex]Substitute for m in Equation 2
[tex]\begin{gathered} 2(\frac{43-3v}{8})+5v=32 \\ \\ \frac{43-3v}{4}+5v=32 \\ \end{gathered}[/tex]To clear the fraction multiply all through by 4
[tex]\begin{gathered} \frac{43-3v}{4}\times4+5v\times4=32\times4 \\ \\ \\ 43-3v+20v=128 \end{gathered}[/tex]Separate the similar term
[tex]\begin{gathered} -3v+20v=128-43 \\ 17v=85 \\ \text{Divide both sides by 17} \\ \frac{17v}{17}=\frac{85}{17} \\ \\ v=5 \end{gathered}[/tex]Substitute for v =5 in equation 3
[tex]\begin{gathered} m=\frac{43-3v}{8}\ldots\text{Equation 3} \\ m=\frac{43-3(5)}{8} \\ m=\frac{43-15}{8} \\ \\ m=\frac{28}{8} \\ \\ m=\frac{7}{2}=3.5 \end{gathered}[/tex]The rental cost for each movie
[tex]m=\text{ \$}3.50[/tex]The rental cost for each video game.
[tex]v=\text{ \$5}[/tex]