Question 201·Medium·Nonlinear Equations in One Variable; Systems in Two Variables

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Consider the system of equations:

\begin{aligned} y &= x^2 - 4x \\[1.4em] y &= 2x - 5 \end{aligned}

Which of the following ordered pairs $(x, y)$ satisfies the system?

A linear-nonlinear system pairs a line with a curve; the $x^2$ term is the cue. Graph both equations in Desmos and click their intersections, where an ordered pair makes both equations true. Then match a point to an option. Checking only the line can mislead you because a point on it might miss the curve.

Hints

Hint 1
The squared $x$ makes one graph a parabola, a U-shaped curve; the other graph is a line. A solution to a system must lie on both graphs. Where should you look?
Hint 2
An intersection is a point where two graphs meet. Click each crossing in Desmos and read its coordinates in $(x,y)$ order before matching it to an option.

Step-by-step

Graph the system
Step 1
Identify what a solution must do
The $x^2$ makes the first graph a parabola, a U-shaped curve; the second graph is a line. So a solution is an intersection, where both graphs meet. A point on only the line doesn't satisfy the system.
Step 2
Read the shared points
Type $y=x^2-4x$ and $y=2x-5$ on separate Desmos lines. Click both intersections: Desmos labels them $(1,-3)$ and $(5,5)$ . The ordered pair $(1,-3)$ is an option and lies on both graphs, so it satisfies the system. Choice A.

Question 201·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