Question 1003·Easy·Math

0 / 2000

\begin{cases} x^{2}-y = 7 \\ y = x - 5 \end{cases}

The ordered pair $(x, y)$ satisfies the system of equations above. Which of the following is a possible value of $x$ ?

A squared variable in a nonlinear system means one graph can bend, so the equations may have more than one shared point. Graph both equations as written in Desmos and click each intersection; every shared point satisfies both equations. Read the coordinate the question asks for, because a point that works in only one equation isn't a solution.

Hints

Hint 1
A system needs a pair that makes both equations true at once. On a graph, such a pair sits where the two graphs meet. Why might a curved graph meet a line more than once?
Hint 2
Desmos can graph the original equations, even when one isn't written as $y=$ . Click each intersection, then read the first number in $(x,y)$ : that's the $x$ -coordinate the question requests.

Step-by-step

Graph both equations in Desmos
Step 1
Graph the first equation
Type $x^2-y=7$ into Desmos. It draws a parabola, a U-shaped curve, because $x$ is squared. One equation isn't enough: a point on this curve may not satisfy the second equation.
Step 2
Find the shared points and read x
Add $y=x-5$ and click both intersections. Desmos shows $(-1,-6)$ and $(2,-3)$ . Each intersection makes both equations true. In $(x,y)$ , $x$ is the first number, so the possible $x$ -values are $-1$ and $2$ . The offered possible value is $-1$ . Choice B.

Question 1003·Easy·Math

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this