A nonlinear system has two equations with the same variables, and at least one graph isn't a straight line. For a circle and a horizontal line, graph both equations in Desmos and click where they cross; each crossing satisfies both equations. Read the coordinate requested, and don't rule out a negative value unless the question does.
Hints
- Hint 1
A solution to a system is a point that makes both equations true. On a graph, look for where the circle and the horizontal line cross. How many crossing points do you see?
- Hint 2
An ordered pair lists first and second. Click each crossing and read its first coordinate. Does the question say that must be positive?
Step-by-step
Approach 1: Graph the circle and line
Step 1Find where the graphs cross
Type and on separate Desmos lines. The first graph is a circle; the second is a horizontal line because its height stays at . The line cuts the circle twice. Each crossing is a solution to both equations.
- Step 2
Read a possible x-value
Click both crossings. Desmos labels them and . In each point , is the first coordinate. Both points work, so is a possible value of ; you don't have to choose the positive one. Choice D.
Approach 2: Substitute the fixed y-value
Step 1Substitute the fixed y-value
The second equation fixes at , so substitution means putting wherever appears in the first equation:
- Step 2
Solve for the square of x
Square the negative number:
Subtract from both sides:
- Step 3
Keep both square roots
The square roots of are the numbers whose squares equal . Since and , keep both signs:
So is a possible value of when . Choice D.