Panphobia said:Homework Statement
x + 3y + z = 4
2x + 2y + z = -1
2x + 3y + z = 3
Find the general solution, and two particular solutions.
The Attempt at a Solution
y = 4; x = -1; z = -7; if I am not mistaken. So how am I supposed to find a general and two particular solutions if there is only one solution?
A system of linear equations is a set of two or more equations that involve two or more unknown variables. The goal is to find the values of the variables that satisfy all the equations in the system.
There are several methods for solving a system of linear equations, including substitution, elimination, and graphing. The most efficient method depends on the specific equations in the system and personal preference.
Yes, a system of linear equations can have one, infinite, or no solutions. One solution means that there is a unique set of values for the variables that satisfy all the equations. Infinite solutions indicate that any set of values that satisfy one equation will also satisfy the others. No solutions mean that there is no set of values that satisfy all the equations.
Solving systems of linear equations is crucial in many fields, including science, engineering, economics, and physics. It allows us to find the relationship between variables, make predictions, and solve real-world problems.
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