Question 122·Medium·Nonlinear Equations in One Variable; Systems in Two Variables

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A system of equations is given by

y = 3x - 2 \qquad\text{and}\qquad y = (x - 4)^2.

One solution to the system satisfies $x < 5$ . What is the value of $x$ ?

Your answer

A squared term can make one graph in a nonlinear system a curve rather than a line. Graph both equations in Desmos and find their intersections, where both equations are true. Use any condition on a coordinate to choose the right intersection before answering. The trap is finding a valid intersection but reporting the wrong point or the wrong coordinate.

Hints

Hint 1
A solution to a system is a point that makes both equations true. On a graph, look for where the line and the curved graph meet. Could they meet more than once?
Hint 2
In an ordered pair $(x,y)$ , the first number is $x$ . Compare the first number at each intersection with the $x$ -condition in the question.

Step-by-step

Graph the two equations
Step 1
Find where the graphs meet
Type $y=3x-2$ and $y=(x-4)^2$ on separate lines in Desmos. The line and the parabola, the U-shaped graph, meet in two places. Each meeting point makes both equations true, so don't stop after finding only one.
Step 2
Choose the x-coordinate that fits
Click both intersections, the points where the graphs meet. Desmos labels them $(2,4)$ and $(9,25)$ . The first number in each pair is $x$ . Only $(2,4)$ has $x<5$ , so the requested value of $x$ is $2$ . Grid in 2.

Question 122·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