Final answer:
A linear system is consistent if there is at least one solution, which occurs when the system's equations do not represent parallel lines. Methods like substitution or elimination can be used to find specific values of x for which the system is consistent.
Step-by-step explanation:
To determine for what value(s) of x a linear system is consistent, we need to have the system of equations. Without the specific equations, we can only provide a general answer. A linear system is consistent if at least one solution exists. This happens when the equations of the system do not represent parallel lines, which would mean there is no point of intersection (no solution), or when they are not the same line (infinite solutions). If the coefficients of x and y in two equations are multiples of each other and the constants are not multiples, the system is inconsistent. If they are not multiples or if the constants are also multiples (meaning they represent the same line), the system is consistent.
If we are provided with specific equations, we can apply methods such as substitution or elimination to find the value(s) of x for which the system has a solution. For example, if we have two equations y = mx + b and ax + by = c, we would solve one of the equations for y and substitute it into the other to find the consistent value(s) of x.