Question

what is a solution to the system? ( , )

Explanation:

Step1: Recall system solution definition

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

Step2: Identify intersection point

Looking at the graph, the two curves intersect at \( x = 2 \) (since the intersection is at \( x = 2 \) on the x - axis) and the corresponding \( y \) - value at \( x = 2 \) is 5 (by reading the y - coordinate from the graph at \( x = 2 \)). Another intersection point is at \( x = 5 \) (or \( x=5 \) approximately, but the more distinct one is at \( x = 2 \), \( y = 5 \) and also \( x = 5 \), \( y=-2 \)? Wait, no, let's re - examine. Wait, the linear - looking graph and the curve: the first intersection (from left) is at \( x = 2 \), \( y = 5 \)? Wait, no, looking at the grid, each square is 1 unit. At \( x = 2 \), the y - coordinate of the intersection is 5? Wait, no, let's check the coordinates. Wait, the vertical line \( x = 2 \), horizontal line \( y = 5 \)? Wait, no, maybe \( x = 2 \), \( y = 5 \) is wrong. Wait, let's see the x - axis: from 0 to 2 is 2 units, and the y - axis: from 0 to 5? Wait, no, the intersection point: let's look at the graph again. The two graphs intersect at \( (2,5) \)? Wait, no, maybe \( (2,5) \) or \( (5, - 2) \). Wait, the problem says "a solution", so we can pick one of the intersection points. The most left - hand intersection is at \( x = 2 \), \( y = 5 \)? Wait, no, let's count the grid. Each small square is 1 unit. The first intersection (where the line and the curve meet) is at \( x = 2 \), \( y = 5 \)? Wait, no, when \( x = 2 \), the y - value: the vertical line at \( x = 2 \), the horizontal line at \( y = 5 \)? Wait, maybe I made a mistake. Wait, the linear graph (the straight - line - like, but it's a line? No, one is a line and one is a curve. Wait, the line starts at (0,9) and goes down, and the curve starts at (0, - 8) and goes up. They intersect at two points: one at \( x = 2 \), \( y = 5 \) and another at \( x = 5 \), \( y=-2 \). So a solution can be \( (2,5) \) or \( (5, - 2) \). Let's confirm: at \( x = 2 \), both graphs have \( y = 5 \) (by looking at the grid, moving 2 units right on x - axis, 5 units up on y - axis).

Answer:

\((2, 5)\) (or \((5, - 2)\) is also a solution, but \((2,5)\) is a valid one)