Question

consider the graph of a system of equations. which point represents a solution to the system of equations? options: (-7,0), (-6,1), (-5,0), (0,7)

Explanation:

Step1: Recall system solution definition

A solution to a system of equations (represented by graphs) is a point where the graphs intersect, as that point satisfies both equations.

Step2: Analyze each option

• Option $(-7,0)$: Check if this point is an intersection. From the graph, the intersection points are not at $x = -7$, $y = 0$.
• Option $(-6,1)$: Visually, the two graphs (a line and a parabola) intersect at $(-6,1)$ (checking the grid, the intersection occurs where $x=-6$ and $y = 1$).
• Option $(-5,0)$: The graphs do not intersect at $x=-5$, $y = 0$.
• Option $(0,7)$: The graphs do not intersect at $x = 0$, $y = 7$.

Answer:

B. $(-6,1)$ (assuming the options are labeled with the second option as $(-6,1)$; if the original options' order is: first $(-7,0)$, second $(-6,1)$, third $(-5,0)$, fourth $(0,7)$, then the correct answer is the second option, $(-6,1)$)