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. In this case, we have a linear equation and a quadratic equation, which can intersect at one, two, or no points, leading to different types of solutions.
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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, allowing for easier solving, especially when one equation is already solved for a variable, as is the case here.
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Quadratic Functions
A quadratic function is a polynomial function of degree two, typically expressed in the form y = ax^2 + bx + c. The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of 'a'. Understanding the properties of quadratic functions is essential for analyzing their intersections with linear functions in a system of equations.
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