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The substitution method is one of the strategies used to solve systems of algebraic equations. This technique involves expressing one variable in terms of another from one equation and substituting this expression into another equation. This helps to reduce a system of equations to a single equation in one variable, which can then be solved using basic algebraic rules.

Here's how the substitution method works in practice:

• Solve one of the equations for one of its variables.
• Substitute the expression obtained in step 1 into the other equation.
• Solve the resulting single-variable equation.
• Back-substitute the found value into one of the original equations to determine the value of the other variable.

In our example, we chose the second equation to solve for y, because it was simpler and led to a straightforward expression of y in terms of x. Substituting this expression into the first equation simplified the system to one equation with one unknown, which was easy to solve.

Algebraic equations are mathematical statements that show the equality of two expressions with one or more unknowns (variables). They are foundational in algebra and form the basis for solving various problems. Equations come in different forms - linear, quadratic, polynomial, and others - each with unique properties and methods of solution.

In the context of our exercise, we dealt with a system of linear algebraic equations. These equations are recognizable by the variables appearing to the first power only and being arranged in a straight line when graphed. By solving algebraic equations, we can find the values of the unknown variables that satisfy all equations simultaneously.

Solving linear equations involves finding the value of the variable that makes the equation true. Linear equations are simple to solve and usually require a few basic steps:

• Isolate the variable on one side of the equation.
• Simplify the equation by combining like terms and reducing fractions if necessary.
• Check the solution by substituting it back into the original equation to ensure it satisfies the equation.

When solving systems of linear equations, multiple methods, including substitution, elimination, and graphing, can be used. In this exercise, we used the substitution method, which reduced our system to a single linear equation that was straightforward to solve. After finding the value of x, we back-substituted into the original equations to find the value of y, hence solving the entire system.