Solve the system of equations at the right by the method of substitution. Verify your results by using a graphing utility. x2+y2-4x+6y-5=0, x+y+5=0

answer: x=-y-5
(-y-5)2+y2-4(-y-5)2+6y-5=0
y=√5-5, y=-5-√5
x+√5-5+5=0
x=-√5
x-5-√5+5=0
x=√5
y=√5-5, y=-5-√5, x=-√5, x=√5

how do i verify this?

graph the equation, see where it crosses the x axis.

which equation do I graph?

Both of them. x2+y2-4x+6y-5=0, x+y+5=0

Most graphing utilities will let you plot one equation over another.

Here is one:
https://www.mathpapa.com/system-calculator.html
Put the equations in, where they overlap is a solution to both.

To verify the solution to the system of equations using a graphing utility, you can follow these steps:

1. Graph the first equation, x^2 + y^2 - 4x + 6y - 5 = 0, and the second equation, x + y + 5 = 0, on the same coordinate plane.

2. If you don't have a graphing utility, you can use online graphing tools like Desmos or GeoGebra to plot the equations. Alternatively, you can use a graphing calculator.

3. Check the point(s) of intersection between the two graphs. These points represent the solution(s) to the system of equations.

4. Compare the points of intersection with the solution obtained by using the method of substitution, which is x = -√5, x = √5, y = √5 - 5, and y = -5 - √5.

5. If the points of intersection match the obtained solution, then the solution is verified. If they don't match, there might be an error in the calculations or on the graph.

By following these steps, you can use a graphing utility to verify the results obtained using the method of substitution.