In a nonlinear system, a squared variable means the graphs may meet more than once. Type both equations into Desmos and click their intersections; each shared point satisfies both equations. Use the sign restriction to choose the right point, then read the coordinate the question asks for. A point can solve both equations and still fail that restriction.
Hints
- Hint 1
A solution to a system makes both equations true. On a graph, it lies where the two graphs cross. Type the equations as written and look for every crossing, not only the first one you see.
- Hint 2
The positive -coordinate belongs to the point right of the -axis. After you click the crossings, which point has its first coordinate greater than ?
Step-by-step
Approach 1: Graph the system in Desmos
- Step 1
Find where the graphs meet
Type and on separate Desmos lines. A solution must satisfy both equations, so it lies where the horizontal line crosses the parabola. The graph shows two crossings.
- Step 2
Choose the positive x-coordinate
Click both crossings. Desmos labels them and . The -coordinate is the first number in each pair. The condition rules out , even though it solves both equations. Keep the point that meets every condition, then read the requested coordinate. The value of is . Choice D.
Approach 2: See why there are two intersections
- Step 1
Replace y with its given value
Use substitution: since the first equation says , put in place of in the second equation:
- Step 2
Isolate the square
Add to both sides:
- Step 3
Find both possible values
A square root of is a number whose square is . Both and work, so keep both for now:
- Step 4
Apply the sign condition
The condition rejects the negative value. So the requested value of is . Choice D.