Determine the solution to each system of equations by...

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Key Concepts

System of Equations

A system of equations consists of two or more equations that share common variables. The goal is to find values for the variables that satisfy all equations simultaneously. Understanding how these equations interact is fundamental to solving problems in algebra.

Substitution Method

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation(s). This reduces the system to a single equation with one variable, which can then be solved directly. This method is particularly useful when one of the equations is easily solvable for one variable.

Dependent Systems and Infinite Solutions

A dependent system occurs when the equations in the system are not independent but rather represent the same underlying relationship, often leading to an identity. In such cases, after substitution, the resulting equation holds true for all values of the variable, implying that there are infinitely many solutions. The solutions can typically be described using a parameter representing one of the variables.

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