Question 205·Medium·Nonlinear Equations in One Variable; Systems in Two Variables
The graphs of a line and a parabola are shown in the -plane. The solutions to the system are the points where the graphs intersect.
Which choice is the sum of the -coordinates of the solutions?
For a system shown by a line and a nonlinear curve, the solutions are exactly the intersection points. On a grid, first locate each intersection, then read the coordinates carefully. Since the question asks for the sum of the -coordinates, ignore the -values except to confirm you are at the correct intersection points.
Hints
Find the solutions visually
Look for the points where the line and the parabola cross each other.
Focus on only
For each intersection point, read its -coordinate from the grid.
Combine the two values
Add the two -coordinates you found.
Desmos Guide
Enter equations that match the graph
From the graph, the parabola has vertex , so enter .
From the graph, the line passes through with slope , so enter .
Find the intersection points
Click on each intersection point of the two graphs to display its coordinates. Record the two -coordinates.
Add the -coordinates
Add the two recorded -coordinates to get the requested sum.
Step-by-step Explanation
Read the intersection points from the graph
The graphs intersect at two grid points:
So the -coordinates of the solutions are and .
Add the -coordinates
Compute the sum: .
Therefore, the sum of the -coordinates of the solutions is .