Question 94·Easy·Nonlinear Equations in One Variable; Systems in Two Variables

0 / 233

x - 4 = 0 \\[1.4em] y = (x - 4)^2 + 1

Which ordered pair $(x, y)$ satisfies the system of equations?

A system of equations asks for one ordered pair that makes both equations true. If one equation fixes the $x$ -coordinate, graph it first. Then graph the other equation in Desmos and click where the graphs meet. Read the point in $(x,y)$ order. Don't treat the $0$ in an equation as the point's $y$ -coordinate: both coordinates must work together.

Hints

Hint 1
An equation containing only $x$ gives every point on its graph the same $x$ -coordinate. What value of $x$ makes the expression on the left equal $0$ ?
Hint 2
A solution to a system lies on both graphs. Add the second equation in Desmos, then click where the graphs meet. The point's first number is $x$ ; what does the second number represent?

Step-by-step

Graph both equations in Desmos
Step 1
Find the required x-coordinate
Type $x-4=0$ into Desmos. Its graph is a vertical line at $x=4$ , so every point that satisfies this equation has $x=4$ .
Step 2
Read the point that satisfies both equations
Add $y=(x-4)^2+1$ on the next Desmos line. Click the intersection, where the graphs meet: Desmos shows $(4,1)$ . A solution to a system must satisfy both equations. The ordered pair is $(4,1)$ , with $x$ first and $y$ second. Choice D.

Question 94·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