Question 205·Medium·Nonlinear Equations in One Variable; Systems in Two Variables

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The graphs of a line and a parabola are shown in the $xy$ -plane. The solutions to the system are the points where the graphs intersect.

Which choice is the sum of the $x$ -coordinates of the solutions?

For a system shown as graphs, each point where the graphs cross is a solution. Read every intersection before doing arithmetic; in a point $(x,y)$ , the $x$ -coordinate comes first. Add those first coordinates, keeping any negative signs. A point where only the parabola crosses an axis is not a solution unless the line passes through it too.

Hints

Hint 1
An intersection is a point shared by both graphs. Look for every place the line and parabola meet, rather than every place the parabola crosses the $x$ -axis. Which points lie on both graphs?
Hint 2
An ordered pair $(x,y)$ lists the horizontal coordinate, $x$ , first. Take that first number from each intersection, including its sign. The question asks you to add those numbers, not multiply them.

Step-by-step

Read the intersections from the graph
Step 1
Read both solutions and their x-coordinates
No Desmos needed. The figure already marks both intersections. A solution is a point both graphs share. The marked crossings are $(-1,0)$ and $(6,7)$ . In an ordered pair $(x,y)$ , $x$ comes first, so their $x$ -coordinates are $-1$ and $6$ . The parabola’s other $x$ -intercept, $(5,0)$ , is not on the line.
Step 2
Add the requested coordinates
Add the two $x$ -coordinates, keeping the negative sign:
$-1+6=5.$
The sum of the $x$ -coordinates of the solutions is $5$ . Choice B.

Question 205·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

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