Solve each system in Exercises 25–26. (x+2)/6 − (y+4)/3 + z/2 = 0, (x+1)/2 + (y−1)/2 − z/4 = 9/2, (x−5)/4 + (y+1)/3 + (z−2)/2 = 19/4

Key Concepts

Systems of Equations

A system of equations consists of two or more equations with the same set of variables. The goal is to find values for the variables that satisfy all equations simultaneously. Solutions can be found using various methods, including substitution, elimination, or matrix operations.

Linear Equations

Linear equations are equations of the first degree, meaning they involve variables raised only to the power of one. They can be represented in the form ax + by + cz = d, where a, b, c, and d are constants. Understanding how to manipulate and solve these equations is crucial for working with systems of equations.

Fractional Coefficients

In the given equations, coefficients are expressed as fractions, which can complicate calculations. It is important to understand how to work with fractions, including finding a common denominator and simplifying expressions, to effectively solve the system of equations.