On the set of axes below, solve the followingsystem of equations graphically and state thecoordinates of all points in the solution set.y = -x² + 6x – 2у 3 2х — 2You can move the parabola by dragging the dots.Graph the line by clicking twice.-10 -9-8-7-6-5-4-3-2-1123.6910-1-23-4-6-7-9-10No solutionsSubmit Answer

Answered: On the set of axes below, solve the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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On the set of axes below, solve the following
system of equations graphically and state the
coordinates of all points in the solution set.
y = -x² + 6x – 2
у 3 2х — 2
You can move the parabola by dragging the dots.
Graph the line by clicking twice.
-10 -9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3.
6
9
10
-1
-2
3
-4
-6
-7
-9
-10
No solutions
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Expert Solution

Step 1

The given equations are:

$y = - x^{2} + 6 x - 2$ and $y = 2 x - 2$

Result: A polynomial of degree $2$ represents a parabola and a polynomial of degree $1$ represents a straight line.

The equation $y = - x^{2} + 6 x - 2$ represents a polynomial and the equation $y = 2 x - 2$ represents a straight line.

Result: If the leading coefficient of the parabola is positive then it is an upward parabola, if the leading coefficient is negative then it is a downward parabola.

Since the leading coefficient of the parabola $y = - x^{2} + 6 x - 2$ is negative, it is a downward parabola.

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