We are going to denote the distance that Elena jogged with [tex]y[/tex], and the distance that Marcus jogged with [tex]x[/tex].
We know that one day, they jogged 15 miles, so the distance Elena jogged plus the distance that Marcus jogged equals 15 miles:
[tex]x+y=15[/tex] This is our equation (1)
We also know that in the same day Elena jogged 1 mile more than Marcus, so the distance Elena jogged equals the distance that Marcus jogged plus one mile:
[tex]x+1=y[/tex] This is our equation (2)
Now that we have our equations setting up, lets arrange them into a system of equations:
[tex] \left \{ {{x+y=15} \atop {x+1=y}} \right. [/tex]
Next we'll solve for [tex]x[/tex] in our equation (2):
[tex]x=y-1[/tex] This is now our equation (3)
Lets replace equation (3) into equation (1) to find the value of [tex]y[/tex]:
[tex]y-1+y=15[/tex]
[tex]2y=16[/tex]
[tex]y=8[/tex]
Finally, now that we know the value of [tex]y[/tex], lets replace it into our equation (3) to find the value of [tex]x[/tex]:
[tex]x=8-1[/tex]
[tex]x=7[/tex]
We can conclude that Elena jogged 8 miles and Marcus jogged 7 miles that day.
