A linear-nonlinear system pairs a line with a curve, often signaled by a squared variable. Graph both equations as written in Desmos; each intersection makes both equations true. A line and a curve may meet more than once, so check every intersection before applying a condition such as positive . Then report the requested coordinate, not the whole point.
Hints
- Hint 1
A solution to a system makes both equations true. On a graph, that means the point must lie on both graphs. Where would you look for such a point?
- Hint 2
A squared variable can give you more than one intersection. Click each one and read its coordinates as , with first. Which first coordinate meets the sign condition?
Step-by-step
Graph both equations and choose the right intersection
Step 1Find where the graphs meet
Type and on separate Desmos lines, exactly as written. Desmos draws a line and a curve with two intersections. An intersection is a point shared by both graphs, so each one satisfies both equations.
- Step 2
Rule out the negative -value
Click the left intersection. Desmos labels it . The first coordinate is , so this point solves the system but fails the positive condition. Changing to would change the point; it wouldn't preserve the solution.
- Step 3
Read the positive -value
Click the right intersection. Desmos labels it . The first coordinate is ; is the -coordinate, which the question doesn't ask for. Choose the intersection that meets the condition, then report the coordinate asked for. The positive value of satisfying the system is . Choice C.