Final answer:
The student's question concerns finding the solution to a system of linear equations, where each point must satisfy all equations to be considered a solution. Linear equations are of the general form y = mx + b, and solutions can be found through substitution, elimination, or graphing methods.
Step-by-step explanation:
The student is dealing with a system of linear equations, which is a collection of two or more linear equations involving the same set of variables. The goal is to find a solution that satisfies all equations in the system. A solution to a system of equations is a set of values for the variables that makes all the equations true. If a point does not satisfy any equation, it's not part of the solution set. If it satisfies one equation but not the other, it is a solution to that particular equation. Finally, if the point satisfies both equations, it represents the intersection point, which is the solution to the entire system.
A linear equation has the general form y = mx + b, where m is the slope and b is the y-intercept. To solve for the intersection of two linear equations, you can use methods such as substitution, elimination, or graphing to find the point where both lines cross. In the context of this question, picking points on a line can be part of the graphing method, where Y₂ and Y₁ are the y-coordinates and X₂ and X₁ are the x-coordinates of the points you choose.