A nonlinear system has two equations sharing and , with a squared variable in at least one. Graph both equations in Desmos and click their intersections: each crossing gives a pair that makes both equations true. If the question requires positive , use that condition before choosing a crossing. A negative crossing can solve the system without answering the question.
Hints
- Hint 1
A solution to a system is a point that makes both equations true. Enter each equation on its own line in Desmos. Where would a point that satisfies both equations appear on the graphs?
- Hint 2
An intersection is where two graphs cross. A line and a curve can cross more than once, so check both crossings. Which one has an -coordinate greater than zero?
Step-by-step
Graph the equations and choose the positive crossing
Step 1Graph the first equation
Type . Desmos draws a line through . Every point on it has a -coordinate twice its -coordinate, so a solution to the system must lie somewhere on this line.
- Step 2
Find the crossing with positive x
Add , then click both intersections, the points where the graphs cross. Desmos shows and . An intersection satisfies both equations, but the positive condition tells you which one to use. The point has , so the requested value is . Choice C.