Question

which statement is true about the solution to the system of equations?
○ the x - value is between 2 and 3, and the y - value is between - 4 and - 5.
○ the x - value is between - 4 and - 5, and the y - value is between 2 and 3.
○ the x - value is between - 2 and - 3, and the y - value is between 4 and 5.
○ the x - value is between 4 and 5, and the y - value is between - 2 and - 3.

Explanation:

Step1: Analyze the intersection point

The solution to a system of linear equations is the point where the two lines intersect. From the graph, we observe the intersection of the red and blue lines.

Step2: Estimate x and y values

Looking at the x - axis, the intersection's x - value is between 2 and 3 (since it's to the right of x = 2 and left of x = 3). For the y - value, looking at the y - axis, the intersection's y - value is between - 4 and - 5 (since it's below y=-4 and above y = - 5? Wait, no, wait. Wait, the blue line is increasing, red is decreasing. Wait, maybe I misread. Wait, the first option: "The x - value is between 2 and 3, and the y - value is between - 4 and - 5". Let's check the graph again. The intersection is in the fourth quadrant? Wait, no, the red line starts from the left (negative x) and goes down, blue line starts from left (negative x, below y = - 5) and goes up. Their intersection: let's see the x - coordinate: between 2 and 3 (since x = 2 to x = 3 on the grid), and y - coordinate: between - 4 and - 5? Wait, maybe. Let's check the options. The first option says x between 2 - 3, y between - 4 and - 5. The other options: x between - 4 - 5 (left of y - axis), but the intersection is to the right of y - axis (positive x? Wait, no, the x - axis: 0 to 5 is positive, left is negative. Wait, the red line starts at x=-5 (left) and goes down, blue line starts left of x = - 5? No, the grid: x from - 5 to 5? Wait, the 0 is in the middle, x = 5 on the right, x=-5 on the left. So the intersection: looking at the x - coordinate, it's between 2 and 3 (since it's between x = 2 and x = 3, positive x). The y - coordinate: between - 4 and - 5? Wait, the blue line is below y=-5 at x=-5, and goes up. The red line is above y=-5 at x=-5 and goes down. Their intersection: when x is between 2 and 3, y is between - 4 and - 5? Let's check the options. The first option is "The x - value is between 2 and 3, and the y - value is between - 4 and - 5". The other options: x between - 4 - 5 (wrong, since intersection is at positive x), x between - 2 - 3 (wrong), x between 4 - 5 (wrong). So the correct option is the first one.

Answer:

The x - value is between 2 and 3, and the y - value is between - 4 and - 5. (The first option: "The x - value is between 2 and 3, and the y - value is between - 4 and - 5.")