Two equations with squared variables form a nonlinear system: a solution must make both equations true. Graph both equations in Desmos, using for the first number and for the second. Because the numbers must be positive, use a crossing where both coordinates are positive. Read the requested expression, not just the point or the sum of the given totals.
Hints
- Hint 1
A system needs the same pair of numbers to satisfy both equations. To graph it, replace with and with in each equation.
- Hint 2
The positive quadrant is the part of the graph where both coordinates are greater than . A crossing there gives a pair that satisfies both equations. Which coordinate represents ?
- Hint 3
A sum of squares means square each number separately, then add. Adding the two totals in the given equations also includes terms that aren't squared.
Step-by-step
Graph the system in Desmos
Step 1Graph both equations
Desmos uses and for its graph axes, so let and . Type and , keeping the same replacements in both equations. Each graph shows pairs that satisfy one equation; where they cross, a pair satisfies both.
- Step 2
Read the positive solution
Click the crossing where both coordinates are positive, as the question requires. Desmos labels it . Since and , this gives and .
- Step 3
Find the sum of the squares
The question asks you to square each number before adding, not to add the two totals from the equations. Type on a new Desmos line; it displays . So . Grid in 13.