The solution to the system of equations is (-1, 1) and (1, -1)
<h3>How to determine the solution to the system of equations?</h3>The system of equations is given as:
x^3 + x^2y + xy^2 + y^3 = 0
x^2 + 4y^2 = 5
The equations in the above system of equations are nonlinear equations.
The best way to a system of equations that are nonlinear equations is by the use of graphs
So, we start by plotting the graphs of the equations in the system of equations given as x^3 + x^2y + xy^2 + y^3 = 0 and x^2 + 4y^2 = 5
See attachment for the graph
The point of intersection represents the solution
From the attached graph, the points of intersection of the equations are
(-1, 1) and (1, -1)
Hence, the solution to the system of equations is (-1, 1) and (1, -1)
Read more about system of equations at:
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Here we are given the x intercepts at x=3 and x=9
So let us try to make quadratic equation for this using given information.
We have factors in the form (x-a)(x-b)
where a and b are x intercepts given to us.
So rewriting in factored form:
Now let us simplify it:
Let us find the vertex now,
For a quadratic equation of the form:
For x coordinate , we have the formula,
So using this formula for our equation,
So x = 6
Answer: The x-coordinate of the parabola's vertex is 6.
