Final answer:
The student is tasked with solving systems of linear equations and arranging the solutions by their x-values. This involves using algebraic techniques to find the intersection point of two lines, checking the solutions, and organizing them accordingly.
Step-by-step explanation:
The student's task involves solving systems of linear equations and arranging their solutions by the increasing x-values. A system has a single solution if the equations represent two lines that intersect at one point.
To solve such systems, you need to look for equations that can be manipulated algebraically to find unique x and y values that satisfy both equations.
The process typically involves steps like substitution or elimination methods. It's also crucial to check the solutions to ensure they satisfy each equation in the system.
Given that we don't have all the specific equations, let's generally discuss how to solve a system of two equations, e.g., '2x + y = 10' and 'x - 3y = -2.'
Arranging the systems of equations with a single solution in increasing order of x-values, we have: 2x - y = 10, x + 3y = -2, -6x + 3y = -2, 2x + y = 4, x + 3y = 5, 6x - y = 11, 2x - y = 10, -6x + 3y = -2.