Answer:
Option 2: (0,-2) and (1,0)
Step-by-step explanation:
Solutions to graphed systems of equations are the places where the graphs overlap/intersect.
For this system of equations, the red and blue graphs overlap at two points.
Since all of the answers are given as ordered pairs, it is important to know what an ordered pair means.
<h3><u>
Ordered pairs</u></h3>
An ordered pair, (x,y), is a pair of numbers, written in parentheses, with a comma between them, that represent the coordinates of a point when graphed on a coordinate system. Each coordinate measures the distance in a certain direction from the origin. The origin is the special point at the intersection of the axes. The axes are the dark horizontal and vertical lines with numbers next to them, representing the value at that distance along the axis.
The first coordinate of an ordered pair is the x-coordinate, and measures the horizontal distance from the origin. Points to the right of the origin are defined to have a positive x-coordinate, and points to the left of the origin are defined to have a negative x-coordinate.
The second coordinate of an ordered pair is the y-coordinate, and measures the vertical distance from the origin. Points above the origin are defined to have a positive y-coordinate, and below the origin are defined to have a negative x-coordinate.
<h3><u>
The intersections</u></h3>
Looking directly below the origin, the blue curve and the red line intersect. Since they intersect directly below the origin, the ordered pair there must have an x-coordinate of zero because no left/right movement was required to get to this point. Only a vertical movement was necessary. The number on the vertical axis tells us that this point has a height of "-2", so the ordered pair for this point is (0,-2).
Looking directly to the right from the origin, the blue curve and the red line intersect again. Since they intersect directly to the right of the origin, the ordered pair there must have a y-coordinate of zero because no up/down movement was required to get to this point. Only a horizontal movement was necessary. The number on the horizontal axis tells us that this point has a horizontal value of "1", so the ordered pair for this point is (1,0).
Since the two points of intersection are (0,-2) and (1,0), the correct answer would be the second choice.
