In Exercises 5–18, solve each system by the substitution method.x = 4y - 2x = 6y + 8

A system of linear equations consists of two or more linear equations that share the same variables. The solution to the system is the point(s) where the equations intersect, representing values that satisfy all equations simultaneously. In this case, we have two equations in terms of x and y, which we need to solve to find their intersection.

The substitution method is a technique for solving systems of equations where one equation is solved for one variable, and that expression is substituted into the other equation. This method simplifies the system into a single equation with one variable, making it easier to solve for the unknowns. In this problem, we can substitute the expression for x from one equation into the other.

Linear functions are mathematical expressions that create straight lines when graphed. They can be represented in the form y = mx + b, where m is the slope and b is the y-intercept. The equations given in the problem represent linear functions in terms of x and y, and understanding their slopes and intercepts can provide insight into their graphical representation and the nature of their intersection.