Since it is given that their balances will be same after x weeks, and since x is common at that point and the value y is also common(same income), then that special point is the solution to those two linear equation as it can satisfy both the equation.
The value of x will be 8 (which means, after 8 weeks, their salary will be on same level)
Their balances after x = 8 weeks will be y = $114
We can use any method like graphing method (in which we take intersection points as solution as they are common to both the graphs), or we use method or substitution (the method that i used below) or method of elimination or many such methods.
We will solve the system of linear equations we got and then that point will give us the needed values.
The given system of equations is
[tex]y = 11.5x + 22\\y =-13x + 218[/tex]
Substituting the value of y from first equation to the second equation, we get:
[tex]y = -13x + 218\\11.5x + 22 = -13x + 218\\\\\text{Adding 13x -22 on both sides}\\\\11.5x + 13x- 22 + 22 = -13x + 13x -22 + 218\\24.5x = 196\\\\\text{Dividing both sides by 24.5}\\\\x = \dfrac{196}{24.5} = 8[/tex]
Thus, after 8 weeks, both of them will be on same salary level until next week comes which might differ their salary.
Putting this value of x in first equation, we get:
[tex]y =11.5x + 22\\y = 11.5 \times 8 + 22\\y = 92 + 22 = 114[/tex]
Thus,
The value of x will be 8 (which means, after 8 weeks, their salary will be on same level)
Their balances after x = 8 weeks will be y = $114
Learn more about system of linear equations here:
: https://brainly.com/question/13722693
