A squared variable beside a linear equation signals a nonlinear system: the same point must satisfy both equations. In Desmos, enter each equation as written and click their intersections; a line and a parabola can meet more than once. Use a condition such as to choose the point, then calculate the requested expression rather than submitting a coordinate.
Hints
- Hint 1
A system is two equations that must hold at the same point. The crossings of their graphs show those points. Why might a curve and a line have more than one crossing?
- Hint 2
In an ordered pair , is the first coordinate. The condition selects a point by its first number, even if another point has a positive second number.
- Hint 3
A product is the result of multiplication. Once you've chosen the point, use its two coordinates for ; the in the line's equation isn't .
Step-by-step
Graph the system in Desmos
Step 1Find the points that satisfy both equations
Type and on separate Desmos lines, without changing their forms. An intersection lies on both graphs, so click both crossings. Desmos shows and . The curve meets the line twice, so you still need the given condition to choose a point.
- Step 2
Choose the point with positive x
In , the first coordinate is . Only has , so keep and . Use the condition to choose the point before computing what the question asks for.
- Step 3
Multiply the chosen coordinates
The product means times . Type on a new Desmos line; it prints . So the value of for the required solution is . Choice C.