Let's solve this problem step-by-step using the given system of equations. Here are the equations:
1. [tex]\( x + y = 200 \)[/tex]
2. [tex]\( x = y - 40 \)[/tex]
We need to find the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] that satisfy both equations.
Step 1: Substitute the expression for [tex]\( x \)[/tex] from the second equation into the first equation.
[tex]\[ x = y - 40 \][/tex]
[tex]\[ (y - 40) + y = 200 \][/tex]
Step 2: Simplify the equation.
[tex]\[ y - 40 + y = 200 \][/tex]
[tex]\[ 2y - 40 = 200 \][/tex]
Step 3: Move the constant term to the other side of the equation.
[tex]\[ 2y - 40 + 40 = 200 + 40 \][/tex]
[tex]\[ 2y = 240 \][/tex]
Step 4: Solve for [tex]\( y \)[/tex].
[tex]\[ y = \frac{240}{2} \][/tex]
[tex]\[ y = 120 \][/tex]
Step 5: Substitute [tex]\( y = 120 \)[/tex] back into the second equation to find [tex]\( x \)[/tex].
[tex]\[ x = y - 40 \][/tex]
[tex]\[ x = 120 - 40 \][/tex]
[tex]\[ x = 80 \][/tex]
So, the solution to the system of equations is [tex]\( x = 80 \)[/tex] and [tex]\( y = 120 \)[/tex].
Therefore, the pair of coordinates representing the solution (in miles) is [tex]\( (80, 120) \)[/tex].
The correct answer is:
B. [tex]\( (80, 120) \)[/tex]
