Question 80·Medium·Nonlinear Equations in One Variable; Systems in Two Variables

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The ordered pair $(x,y)$ satisfies the system of equations

\begin{cases} x^2 + y = 38 \\ y - 3x = -2 \end{cases}

and $x > 0$ . What is the value of $y$ ?

Your answer

A squared variable in a system means the graphs can meet at more than one point. Graph both equations as written in Desmos and click their intersections; each meeting point satisfies both equations. Apply the condition on $x$ before choosing a point, then read the coordinate the question asks for. The tempting slip is to submit $x$ when the question wants $y$ .

Hints

Hint 1
An intersection is a point shared by both graphs, so its coordinates make both equations true. Type the equations on separate Desmos lines and click each crossing. Does either point have a negative first coordinate?
Hint 2
In an ordered pair $(x,y)$ , $x$ is the first coordinate and $y$ is the second. Use the first coordinate to decide which intersection meets $x>0$ . Which coordinate should you submit after that?

Step-by-step

Graph both equations and choose the right intersection
Step 1
Rule out the intersection with negative $x$
Type $x^2+y=38$ and $y-3x=-2$ on separate Desmos lines. An intersection lies on both graphs, so it satisfies both equations. Click the left crossing: Desmos shows $(-8,-26)$ . Its first coordinate is negative, so $x>0$ rules it out.
Step 2
Read $y$ at the remaining intersection
Click the other intersection. Desmos shows $(5,13)$ ; its first coordinate, $x=5$ , meets $x>0$ . In the ordered pair $(x,y)$ , $y$ is the second coordinate. Use $x$ to choose the point, but submit $y$ . The requested value is $13$ , not $5$ . Grid in 13.

Question 80·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