Among (-1, 0), (-1, -1), (1, 0), and (1, -1), the point (1, -1) is the best estimate for the solution. It's closest to the intersection point, being 0 units right and 2 units down from it.
Identify the Point of Intersection: Look at the graph where the lines representing the equations intersect. This intersection point represents the solution to the system of equations.
Compare Given Coordinate Pairs: Evaluate the provided coordinate pairs (-1, 0), (-1, -1), (1, 0), and (1, -1) in relation to the point of intersection.
Calculate Distances: Measure the distances between each provided coordinate and the point of intersection in terms of units right/left and up/down.
Select the Closest Point: Determine which coordinate pair is the closest to the point of intersection based on the calculated distances. The coordinate pair that is nearest to the intersection point is the best estimate for the solution.
Let's break down the distances for each coordinate pair compared to the point of intersection (1, -1):
(-1, 0): This point is 2 units to the left and 1 unit up from the point of intersection.
(-1, -1): This point is 2 units to the left and 2 units down from the point of intersection.
(1, 0): This point is 0 units to the right and 1 unit up from the point of intersection.
(1, -1): This point is 0 units to the right and 2 units down from the point of intersection.
From these calculations, it's clear that (1, -1) is the closest point to the intersection, being 0 units right and 2 units down. Therefore, based on the proximity to the point of intersection, (1, -1) is the best estimate for the solution to the system of equations.
complete the question
"Given a system of equations graphed on a coordinate plane where the two lines intersect at the point (1, -1), which of the following coordinate pairs—(-1, 0), (-1, -1), (1, 0), (1, -1)—is the best estimate for the solution to the system of equations based on their proximity to the point of intersection?"