Show all work to verify if the given point is a solution to the system of equations. ### System of Equations and PointsWe have a system of two equations given by:\[ 5x^2 - y^2 = 3 \]\[ x^2 + 2y^2 = 5 \]Additionally, we have a specific point mentioned:\[ \text{Point:} \left( -1, -\sqrt{2} \right) \]#### Explanation:1. **Equation 1: $5x^2 - y^2 = 3$** - This equation represents a conic section known as a hyperbola when both $x$ and $y$ are real numbers.2. **Equation 2: $x^2 + 2y^2 = 5$** - This equation represents an ellipse when both $x$ and $y$ are real numbers.3. **Point: $\left( -1, -\sqrt{2} \right)$** - This is a specific point in the Cartesian coordinate system which can be tested for its position relative to the conic sections defined by the above equations.#### Graphical Representation:To understand how these equations and points relate to each other, we would typically plot them on the Cartesian plane:- **Hyperbola:** - The hyperbola will have branches depending on the values of $x$ and $y$ that satisfy the first equation.- **Ellipse:** - The ellipse will have its shape determined by the second equation, showing an oval-like figure on the graph.### AnalysisVerifying if the given point $\left( -1, -\sqrt{2} \right)$ lies on either or both of the curves involves substituting $x = -1$ and $y = -\sqrt{2}$ into each of the equations.1. **Substitute into Equation 1:** \[5(-1)^2 - (-\sqrt{2})^2 = 5 - 2 = 3 \] - Satisfies the first equation.2. **Substitute into Equation 2:** \[(-1)^2 + 2(-\sqrt{2})^2 = 1 + 4 = 5 \] - Satisfies the second equation.Since the point \(\left( -1, -\sqrt{2} \right)\

The given system of equations,The given point .We have to check the point is a solution to the…

Answered: 5x² - y² = 3 2 x² + 2y² = 5 Point: -1,…

5x² - y² = 3 2 x² + 2y² = 5 Point: -1, -√2

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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