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 common variables. In this case, the system includes a quadratic equation (2x^2 = 3y + 23) and a linear equation (y = 2x - 5). Solutions to the system are the points where the graphs of these equations intersect, indicating values of x and y that satisfy both equations simultaneously.
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Substitution Method
The substitution method is a technique used to solve systems of equations by replacing one variable with an expression derived from another equation. In this context, substituting the x-values of the intersection points (0, -1) and (3, 6) into both equations allows us to verify whether these points are indeed solutions of the system.
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Graphical Interpretation
Graphical interpretation involves analyzing the visual representation of equations on a coordinate plane. The graph shows the intersection points of the quadratic and linear equations, which represent the solutions to the system. Understanding how to read and interpret these graphs is crucial for confirming the validity of the solutions found through substitution.
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