Verify that the points of intersection specified on the...

Verify that the points of intersection specified on the graph of each nonlinear system are solutions of the system by substituting directly into both equations.
$$
\begin{aligned}
2 x^{2} &=3 y+23 \\
y &=2 x-5
\end{aligned}
$$

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Key Concepts

Verification of Solutions

Verification of solutions is the process of confirming that a candidate point satisfies all equations within a system. This is done by substituting the point's coordinates into each equation to ensure that the resulting equalities hold true, thereby validating the solution.

Substitution Method

The substitution method involves solving one equation for a variable and then substituting that expression into the other equation(s). This reduces the number of variables and simplifies the system into a more manageable form, typically leading to an equation in one variable that can be solved.

Intersection of Graphs

Intersection of graphs refers to a point or set of points where two curves meet. At these intersections, both equations have the same coordinate values, meaning that the point satisfies both equations of the system simultaneously.

Nonlinear Systems

Nonlinear systems involve one or more equations that are not linear. These systems often include terms like squares, products, or other nonlinear expressions. Solving such systems can be more challenging than linear ones and may require techniques like substitution or numerical methods.

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