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 that share the same variables. The goal is to find the values of these variables that satisfy all equations simultaneously. In this case, the system includes two equations involving the variables x and y, which can be solved using various methods such as substitution, elimination, or graphical representation.
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Quadratic Equations
Quadratic equations are polynomial equations of degree two, typically in the form ax^2 + bx + c = 0. In the given system, the first equation is quadratic in x, which means it can have zero, one, or two solutions for x depending on the discriminant. Understanding how to manipulate and solve quadratic equations is essential for finding the values of x and y in the system.
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Substitution Method
The substitution method is a technique for solving systems of equations where one equation is solved for one variable, and that expression is substituted into the other equation. This method simplifies the system, making it easier to solve for the remaining variable. In this problem, applying substitution can help isolate one variable and find the corresponding values for both x and y.
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