Answer
System of equations is
y = x + 15
y = 2x + 5
x = 10 windows, y = $25
The solution means that the total charge and number of windows washed for both of them will be the same when each of them washes 10 windows and gets 25 dollars as total charge.
The number of windows to be washed is more than 10, then Jacques is the better alternative as the his total charge only increases by 1 dollar at this point, for every rise in the number of windows washed.
The number of windows to be washed is less than 10, then Ray is the better alternative as the his total charge is lower for number of windows in this range due to his initial charge, ($5), being far less than Jacques' own.
Step-by-step explanation
y is the total charge for washing the windows of the house and x is the number of windows washed.
For Jacques, $15 charge + $1 per window,
If x windows are washed, Jacques' total charge will be
y = 15 + x
y = x + 15
For Ray, $5 charge + $2 per window,
If x windows are washed, Ray's total charge will be
y = 5 + 2x
y = 2x + 5
The two equations written together as a system of equation will now be
y = x + 15
y = 2x + 5
We are then told to solve this to obtain when their total charge and number of windows washed will match each other
Since, y = y
y = x + 15
y = 2x + 5
x + 15 = 2x + 5
2x + 5 = x + 15
2x - x = 15 - 5
x = 10 windows
When x = 10
y = x + 15
y = 10 + 15 = 25 dollars
The solution means that the total charge and number of windows washed for both of them will be the same when each of them washes 10 windows and gets $25 as total charge.
Looking at the setup, we can see that when the number of windows to be washed is more than 10, then Jacques is the better alternative as the his total charge only increases by 1 dollar at this point, for every rise in the number of windows washed.
The number of windows to be washed is less than 10, then Ray is the better alternative as the his total charge is lower for number of windows in this range due to his initial charge, ($5), being far less than Jacques' own.
Hope this Helps!!!