Final answer:
The question involves solving a system of equations by rewriting them in terms of the variables A = 1/x and B = 1/y, and then using substitution or elimination methods to find A and B. Once these are found, x and y can be calculated as their reciprocals.
Step-by-step explanation:
Solving a System of Equations
The given system of equations is:
- 9/x - 4/y = 8
- 13/x + 7/y = 101
To solve these equations, we can first try to find common terms. In the second equation, there seems to be an error as it contains two terms with x but it's likely that the second term is meant to be with respect to y, so it should be 13/x + 7/y = 101. We'll assume this is the correct equation.
Let's denote A = 1/x and B = 1/y, rewriting the equations in terms of A and B:
9A - 4B = 8
- 13A + 7B = 101
Now, we can use the method of substitution or elimination to solve for A and B. Once A and B are found, we can calculate x and y by taking the reciprocals: x = 1/A and y = 1/B.
This is akin to lines on a graph where x and y values are dependent on the equation like y = 9 + 3x, which represents a line with a slope of 3 and a y-intercept of 9. We can also draw parallels to our equations as in the linear equations mentioned earlier such as 7 y = 6x + 8, or the dependent and independent variable relationship like the flu cases depending on the year.