Question 148·Easy·Nonlinear Equations in One Variable; Systems in Two Variables

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Solve the system of equations:

\begin{aligned} y &= |x-2| + 1 \\[1.4em] y &= -x + 7 \end{aligned}

What is the solution $(x,y)$ ?

An absolute-value system pairs a V-shaped graph with another equation using the same $x$ and $y$ . Type both equations into Desmos as written, then click their intersections. Each shared point satisfies both equations. Keep the absolute-value bars: removing them turns the V into a line and can give you the wrong point.

Hints

Hint 1
The absolute value $|x-2|$ is the distance from $x$ to $2$ . Its graph bends into a V rather than continuing as one straight line, so keep the bars when you enter the first equation.
Hint 2
A solution to a system is one $(x,y)$ pair that fits both equations. On a graph, look for a point shared by the V and the line. What does Desmos show when you click it?

Step-by-step

Graph both equations
Step 1
Graph the absolute-value equation
Type $y=|x-2|+1$ into Desmos. It draws a V: absolute value makes $|x-2|$ nonnegative even when $x<2$ . Don't drop the bars, or you'll lose the left side of the graph.
Step 2
Read the shared point
Add $y=-x+7$ and click each intersection. Desmos labels the sole shared point $(4,3)$ . An intersection lies on both graphs, so the solution is $(4,3)$ . Choice D.

Question 148·Easy·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