Let x be the number of beverages and food; therefore, the two equations that model Jack's and Joshua's expenditures are
[tex]\begin{gathered} Ja=10+1x \\ Jo=5+4x \end{gathered}[/tex]In order to graph both linear equations, we need two points on each of them. Finding the points,
[tex]\begin{gathered} x=0\Rightarrow Ja=10+1\cdot0=10 \\ (0,10) \\ x=1\Rightarrow Ja=10+1\cdot1=11 \\ \Rightarrow(1,11) \\ \text{and} \\ x=0\Rightarrow Jo=5+4\cdot0=5 \\ \Rightarrow(0,5) \\ x=1\Rightarrow Jo=5+4\cdot1=9 \\ \Rightarrow(1,9) \end{gathered}[/tex]Therefore, the graph of the two lines simultaneously is
The intersection point is (5/3, 35/3). Therefore, the answer is 5/3 beverages and food
