Verify that the values of the variables listed are solutions of the system of equations. { 3 x+3

step 1 So let's check the solution. The solution is 1, negative 1, 2. This is X, Y, and Z. So let's go

Verify that the values of the variables listed are solutions...

Key Concepts

Consistency of Equations

Consistency in a system of linear equations means that there exists at least one set of values for the variables that satisfies all the equations simultaneously. A consistent system may have a unique solution, infinitely many solutions, or sometimes none (if contradictory conditions are present), making it essential to ascertain consistency when solving or verifying a solution.

System of Linear Equations

A system of linear equations consists of multiple linear equations that share common variables. The objective is to find values for these variables that simultaneously satisfy every equation in the system. Systems like these form the foundation of many problems in algebra and are pivotal for modeling relationships between multiple quantities.

Verification of Solutions

Verification of solutions involves substituting proposed values for the variables back into each equation of the system to check whether all equations hold true. This is a crucial step that confirms the accuracy of an alleged solution, ensuring that it meets all the criteria imposed by the system.

Substitution Method

The substitution method is a common approach for solving systems of equations. It involves expressing one variable in terms of others using one of the equations, and then substituting this expression into the remaining equations. This technique simplifies the system, reducing it to fewer variables and making it easier to find or verify the solution.

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