Ok, so
We have the next system of equations:
The first equation is a line, and the second one is a parable.
If we graph, we would get the following:
Then, we notice that there's two intersection points between both graphs.
These points are located at ( -1 , -3 ), and ( 2 , -6)
Therefore, there are two solutions for this problem.
x = -1 and y = -3,
x = 2, and y = -6
Now, how to graph each equation?
First one, take the line y = -x-4
Notice that this equation tells us that the line given has its intersection with y-axis at ( 0 , -4 )
We also know that a line is formed with two points, so we could replace by any "x" number and see which value "y" takes.
For example:
If x = 1,
y = -1-4, which is y = -5
So we got other point: ( 1, -5).
Now, we just join both points and we get the line, like this:
And that's how you can graph the line.
Now, how could we graph the parable?
We know that we have to take three points to join to graph a parable. So, first, we would find its intersections with x - axis, if we equal the equation to zero.
x² – 2x - 6 = 0
If we solve this equation, we obtain that x could take two different values.
To solve it, we use the next equation:
x = 1 - √7 or
x = 1 + √7.
Then, we actually have two points.
Now, finally, we could find its vertex.
If we find the vertex of the parable, we notice that it is located in (1,-7)
Now, we just join these three points as this:
And if we put these graphs together, we obtain the first graph I drew, and notice that the solution for the system is the intersection between both functions.