Question 79·Easy·Nonlinear Equations in One Variable; Systems in Two Variables

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Consider the system of equations

y = x + 1

x^2 + y^2 = 25

Which ordered pair $(x, y)$ satisfies the system and lies in the first quadrant?

A system of equations asks for a point that makes both equations true. Graphing a line and a circle in Desmos shows where they intersect, but there may be more than one crossing. The first-quadrant condition keeps only a point with both coordinates positive. A point on the circle alone isn't enough; it must also lie on the line.

Hints

Hint 1
In the first quadrant, both coordinates are greater than $0$ . A point on an axis doesn't count. Which choices can you rule out before solving the system?
Hint 2
An intersection lies on both graphs, so it satisfies both equations. Type the line and circle into Desmos as written, then click their crossings. Which crossing has positive $x$ and $y$ ?

Step-by-step

Filter the choices, then graph the system
Step 1
Apply the quadrant condition
The first quadrant means $x>0$ and $y>0$ . So $(-4,-3)$ has the wrong signs, and $(0,5)$ lies on an axis because $x=0$ . Neither can be the requested point.
Step 2
Find the point on both graphs
Type $y=x+1$ and $x^2+y^2=25$ on separate lines. Click both crossings; Desmos shows $(-4,-3)$ and $(3,4)$ . Each intersection satisfies both equations, but only $(3,4)$ has two positive coordinates. Find the system's solutions, then use the extra condition to choose. The ordered pair is $(3,4)$ . Choice D.

Question 79·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