Explanation: The given topic is about a system of equations represented by -2r + 5y = 19 and y = -(r - 1). The graph provided helps in approximating the solution to this system.
In the given system of equations: -2r + 5y = 19 y = -(r - 1)
We can solve this system of equations by substituting the value of y from the second equation into the first equation. This will allow us to solve for the value of r.
Substituting y = -(r - 1) into -2r + 5y = 19, we get: -2r + 5(-(r - 1)) = 19
Simplifying the equation: -2r - 5r + 5 = 19 -7r + 5 = 19
Now, let's solve for r:
Subtracting 5 from both sides of the equation: -7r = 14
Dividing both sides by -7: r = -2
Now that we have found the value of r, we can substitute it back into the second equation to find the corresponding value of y.
Using y = -(r - 1), we substitute r = -2: y = -(-2 - 1) y = -(-3) y = 3
Therefore, the solution to the system of equations is r = -2 and y = 3.
Looking at the graph, we can approximate the solution by finding the point where the two lines intersect. Based on the graph, the approximate solution is (-2, 3).
So, the correct answer is A. (-1, 4)