A squared alongside a line signals a nonlinear system: the graphs may meet more than once. Graph both equations in Desmos and click their intersections. Each shared point satisfies both equations, but the question asks for only one coordinate. Check that the first coordinate is positive before submitting it; zero doesn't count as positive.
Hints
- Hint 1
An intersection is a point where two graphs meet, so its coordinates make both equations true. Graph each equation on its own Desmos line. How many places do the graphs meet?
- Hint 2
In a point , the first coordinate is . Click each intersection and check that first number. A point can solve both equations and still fail the requirement that be positive.
Step-by-step
Graph the system and choose the positive x-value
Step 1Find where the graphs meet
Type and on separate Desmos lines. The squared expression makes the first graph a parabola, a U-shaped curve. Desmos shows two crossings with the line. Each crossing solves the system because it lies on both graphs.
- Step 2
Rule out the left intersection
Click the left intersection. Desmos labels it , so its -coordinate, the first number, is . This point solves both equations, but isn't positive.
- Step 3
Read the positive x-value
Click the right intersection. Desmos labels it . The first coordinate is , which is positive; is , not what the question asks for. Read the requested coordinate, not the whole point. The positive value of satisfying the system is . Grid in 5.