Question 207·Medium·Nonlinear Equations in One Variable; Systems in Two Variables

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x^2 - y = 4

y = 2x - 4

A solution to the system of equations is $(x,y)$ . Which of the following is a possible value of $x - y$ ?

A squared variable alongside a line signals a nonlinear system: the graphs may meet more than once. Type both equations into Desmos and click their intersections, since each shared point satisfies both equations. Then use the two coordinates from the same point to find the requested expression. Watch the subtraction order: $x-y$ is not $y-x$ .

Hints

Hint 1
A solution to a system is a point that makes both equations true. On a graph, that's where the two graphs meet. How many intersections do you see?
Hint 2
Each intersection gives an $(x,y)$ pair, with $x$ first. Find $x-y$ for each pair; subtracting in the opposite order changes the result.

Step-by-step

Graph the system in Desmos
Step 1
Find the shared points
Type both equations as written into Desmos and click each intersection. Desmos shows $(0,-4)$ and $(2,0)$ . Each is a solution to the system because it lies on both graphs.
Step 2
Find the possible differences
The question asks for $x-y$ , so type $0-(-4)$ for the first point and $2-0$ for the second. Desmos shows $4$ and $2$ . Keep $x$ and $y$ from the same intersection. Since $2$ is listed, it is a possible value of $x-y$ . Choice C.

Question 207·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