Question 197·Medium·Nonlinear Equations in One Variable; Systems in Two Variables

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The system of equations is given below:

x + y = 10 \\[1.4em] x^2 + y^2 = 58

If $(x, y)$ is a solution to the system above, what is one possible value of $x$ ?

A nonlinear system has two equations with the same variables and a squared term in at least one. Graph both equations in Desmos and click where they cross: each crossing gives a pair that satisfies both equations. If the question asks for $x$ , read the first coordinate. A pair that satisfies only the simpler equation isn't enough.

Hints

Hint 1
A solution to a system must make both equations true. On a graph, that means the point lies on both graphs. Where can you find the points that satisfy both conditions?
Hint 2
An ordered pair $(x,y)$ lists $x$ first and $y$ second. The graphs may cross more than once, but the question asks for one possible value of $x$ , not the whole pair.

Step-by-step

Graph the system and read an intersection
Step 1
Graph both equations
Type $x+y=10$ and $x^2+y^2=58$ on separate Desmos lines. Desmos draws a line and a circle with two crossing points. Each intersection makes both equations true at once. Checking the line alone can leave you with a pair that misses the circle.
Step 2
Read the requested coordinate
Click both intersections. Desmos labels them $(3,7)$ and $(7,3)$ . In $(7,3)$ , the first coordinate is $x$ , so one possible value of $x$ is $7$ . Choice A.

Question 197·Medium·Nonlinear Equations in One Variable; Systems in Two Variables

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this