Final Answer:
w = 1, x = 2, y = 1, z = -1 .Solving the system of equations yields w = 1, x = 2, y = 1, and z = -1, satisfying all four equations concurrently through methods like substitution or elimination.
Step-by-step explanation:
By solving the given system of equations, the solution is w = 1, x = 2, y = 1, and z = -1. This solution satisfies all four equations simultaneously. The solution was obtained through methods like substitution, elimination, or matrix operations to find the values of the variables.
In the first equation, the coefficients of w, x, y, and the constant term are matched to those in the other equations, creating a system of linear equations. Solving this system involves manipulating the equations to isolate and determine the values of each variable. The obtained solution (w = 1, x = 2, y = 1, z = -1) makes all four equations true.
The solution represents the intersection point of four planes in a four-dimensional space, where each equation corresponds to a plane. These planes intersect at the specific values of w, x, y, and z, satisfying the entire system. This process of solving systems of linear equations is fundamental in algebra and has applications in various fields, including physics, engineering, and economics.