A system of equations asks for a point that makes both equations true. Graphing a line and a circle in Desmos shows where they intersect, but there may be more than one crossing. The first-quadrant condition keeps only a point with both coordinates positive. A point on the circle alone isn't enough; it must also lie on the line.
Hints
- Hint 1
In the first quadrant, both coordinates are greater than . A point on an axis doesn't count. Which choices can you rule out before solving the system?
- Hint 2
An intersection lies on both graphs, so it satisfies both equations. Type the line and circle into Desmos as written, then click their crossings. Which crossing has positive and ?
Step-by-step
Filter the choices, then graph the system
Step 1Apply the quadrant condition
The first quadrant means and . So has the wrong signs, and lies on an axis because . Neither can be the requested point.
- Step 2
Find the point on both graphs
Type and on separate lines. Click both crossings; Desmos shows and . Each intersection satisfies both equations, but only has two positive coordinates. Find the system's solutions, then use the extra condition to choose. The ordered pair is . Choice D.