Question 151·Easy·Nonlinear Equations in One Variable; Systems in Two Variables

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3x + 6 = 0 \\[1.4em] y = (x + 5)^2

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

A system of equations asks for an ordered pair that makes both equations true. If one equation contains only $x$ , it fixes the first coordinate. Graph both equations in Desmos and click where they meet. Be careful to use that same $x$ -value when finding $y$ .

Hints

Hint 1
A solution must work in both equations. The first equation contains no $y$ , so it fixes the first coordinate of the pair. What $x$ -value does its vertical line show in Desmos?
Hint 2
Where the graphs meet, the second equation uses the same $x$ -value found from the first. Click that point and read its coordinates in order: $x$ first, then $y$ .

Step-by-step

Graph both equations
Step 1
Find the required x-coordinate
Type $3x+6=0$ into Desmos. It draws a vertical line crossing the $x$ -axis at $-2$ , so every solution has $x=-2$ . Losing the minus sign would give $x=2$ , which does not satisfy this equation.
Step 2
Read the point on both graphs
Add $y=(x+5)^2$ and click where the graphs meet. Desmos labels the point $(-2,9)$ . A solution to a system must make both equations true with the same $x$ : the first coordinate is $-2$ , and the square gives a positive second coordinate, $9$ . So the ordered pair that satisfies the system is $(-2,9)$ . Choice C.

Question 151·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