Question 227·Medium·Nonlinear Equations in One Variable; Systems in Two Variables

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\begin{aligned} 2x + y &= 5 \\[1.4em] x^2 + y^2 &= 10 \end{aligned}

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

Your answer

A linear-nonlinear system pairs a line with a curve, so it can have more than one solution. Type both equations into Desmos as written and click every intersection; each shared point satisfies both equations. Then compare the coordinate the question asks for. Reading the other coordinate can undo an otherwise correct graph.

Hints

Hint 1
A solution to a system is a pair $(x,y)$ that satisfies both equations. On a graph, that means a point where the line and circle meet. Look for every place they meet, not only the first one you see.
Hint 2
In a pair $(x,y)$ , the first coordinate is $x$ and the second is $y$ . After clicking each intersection, write down the first number in each pair. Which of those numbers is greater?

Step-by-step

Graph the two equations
Step 1
Find every solution
Type $2x+y=5$ and $x^2+y^2=10$ on separate lines in Desmos. It draws a line and a circle with two intersections. Each intersection lies on both graphs, so each point satisfies both equations.
Step 2
Compare the requested coordinates
Click both intersections to read their coordinates: $(1,3)$ and $(3,-1)$ . In $(x,y)$ , $x$ is the first coordinate. Compare that coordinate at every intersection, not the largest number you see in a pair. The possible $x$ -values are $1$ and $3$ , so the greater possible value of $x$ is $3$ . Grid in 3.

Question 227·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