The squared variable marks a nonlinear system, which may have more than one solution. When one equation gives you directly, use substitution to replace in the other equation. Then solve for in Desmos, restricting the result to positive values if the question requires one. Don’t assume a squared equation has only one solution.
Hints
- Hint 1
Use substitution when one variable is already by itself: replace that variable in the other equation with the value it equals. What equation remains after you replace ?
- Hint 2
A square gives the same result for a positive number and its negative. So the new equation may give two -values. How can you tell Desmos to keep only the positive one?
Step-by-step
Substitute, then solve in Desmos
Step 1Replace with its given value
Since , use substitution to put in place of in the first equation: . The same pair of values must make both equations true, so this leaves one equation to solve for .
- Step 2
Find the positive -value
Type in Desmos. Use because Desmos graphs ; tells it to find a value that makes the sides equal. The restriction keeps only positive values. Under PARAMETERS, Desmos shows . The squared term also allows , but that isn't positive. So the requested value of is . Grid in 2.