Question 1024·Medium·Math

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The variables $x$ and $y$ satisfy the system of equations

\begin{cases} x^{2}+y=7\\ y^{2}+x=11 \end{cases}

If $x$ and $y$ are both positive, what is the value of $y$ ?

Your answer

Squared variables signal a nonlinear system: the equations graph as curves that may cross more than once. Enter both equations in Desmos and find a crossing, since its coordinates satisfy both equations. If both variables must be positive, look in the first quadrant, where both coordinates are positive. Then report the coordinate the question asks for, not the other one.

Hints

Hint 1
A solution to a system is a pair of values that makes both equations true. On a graph, that pair appears where the two curves cross. You can enter each equation in Desmos exactly as written.
Hint 2
The first quadrant is right of the vertical axis and above the horizontal axis, so both coordinates are positive there. After clicking the crossing in that region, which coordinate gives the requested $y$ -value?

Step-by-step

Find the positive intersection
Step 1
Locate the region where both values are positive
Both positive means $x>0$ and $y>0$ . On a graph, those points are in the first quadrant, right of the vertical axis and above the horizontal axis. So look for a crossing in that region.
Step 2
Graph the system and read the requested coordinate
Type $x^{2}+y=7$ and $y^{2}+x=11$ on separate Desmos lines. A solution lies on both graphs, so it appears where they cross. Click the first-quadrant crossing; Desmos labels it $(2,3)$ . The second coordinate is $y$ , so $y=3$ . Grid in 3.

Question 1024·Medium·Math

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this