Here are the essential concepts you must grasp in order to answer the question correctly.
Systems of Equations
A system of equations consists of two or more equations with the same variables. The goal is to find the values of the variables that satisfy all equations simultaneously. Methods for solving systems include substitution, elimination, and graphical representation. Understanding how to manipulate and solve these equations is crucial for finding the correct solution.
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Substitution Method
The substitution method involves solving one equation for a variable and then substituting that expression into another equation. This technique simplifies the system, making it easier to solve for the remaining variables. In this problem, the hint suggests substituting 1/x with t and 1/y with u, which transforms the equations into a more manageable form.
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Variable Transformation
Variable transformation is a technique used to simplify complex equations by substituting new variables for existing ones. In this case, letting 1/x = t and 1/y = u allows the original equations to be rewritten in terms of t and u, which can simplify the solving process. This approach can make it easier to identify relationships and solve the system of equations.
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