Solve the question give in image and explain the answer---**Question Stem:** The system of linear equations represented by the lines l and m is **Chart/Diagram Description:** * **Type:** Coordinate plane with two intersecting lines. * **Coordinate Axes:** X-axis and Y-axis are labeled. Arrows indicate positive direction. The origin (0,0) is implicitly where the axes intersect. * **Lines:** Two lines, labeled 'l' and 'm', are shown. * Line 'l' has a negative slope and passes through the point (0,2) and a point to the left and below (0,2). * Line 'm' has a positive slope and passes through the point (0,2) and a point to the right and below (0,2). * Lines 'l' and 'm' intersect at the point (0,2). * **Points:** * (0,2) is labeled and appears to be the intersection point of lines l and m. * (-1,0) is labeled on the negative X-axis. * (3/2,0) is labeled on the positive X-axis. * **Other Labels:** An angle labeled 'a' is shown between line m and the negative Y-axis. **Options:** (A) consistent with unique solution (B) inconsistent (C) consistent with three solutions (D) consistent with many solutions

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We have a coordinate plane showing two lines labeled l and m. Line l has a negative slope and line m has a positive slope. Both lines intersect at the point zero comma two. We need to determine what type of solution this system of linear equations has. The key concept here is that the solution to a system of linear equations is found where the lines intersect. Looking at our graph, we can observe that lines l and m intersect at exactly one point, which is zero comma two. Therefore, this system has exactly one solution. Let me explain the different types of solutions for linear systems. A system is consistent if it has at least one solution, and inconsistent if it has no solution. When two lines intersect at exactly one point, we have a unique solution. When lines are parallel and distinct, there is no solution. When lines are identical, there are infinite solutions. In our case, since the lines intersect at one point, we have a consistent system with a unique solution. Let's analyze this linear system problem. We have two lines, l and m, shown on a coordinate plane. Line l has a negative slope and line m has a positive slope. Both lines intersect at the point zero comma two. We can also see that line l passes through negative one comma zero, and line m passes through three halves comma zero. Before analyzing our specific problem, let's review the types of linear systems. A consistent system with a unique solution occurs when two distinct lines intersect at exactly one point. An inconsistent system occurs when two parallel lines never intersect, meaning no solution exists. A consistent system with many solutions occurs when two lines are identical and overlap completely, creating infinitely many solutions. Note that option C, three solutions, is impossible for linear systems. Now let's analyze our specific system. We can observe that lines l and m are distinct lines with different slopes. Line l has a negative slope while line m has a positive slope. Most importantly, they intersect at exactly one point: zero comma two. Since two distinct lines can intersect at most once, this is the only intersection point. Therefore, our system is consistent with a unique solution. Now let's verify our answer. We have two distinct lines that intersect at the point zero comma two. This means exactly one solution exists, making the system consistent with a unique solution. Therefore, the correct answer is option A: consistent with unique solution. To summarize what we have learned: Linear systems can have three possible outcomes - a unique solution, no solution, or infinite solutions. When two distinct lines intersect at exactly one point, the system has a unique solution and is called consistent. In our problem, the lines intersect at zero comma two, making it a consistent system with a unique solution. Therefore, the correct answer is option A.