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The substitution method is one of the ways to solve a system of linear equations. This method involves solving one of the equations for one variable and then substituting this expression into the other equation.
This allows you to find the value of one variable, which can then be substituted back into the expression to find the value of the other variable.
By breaking down the equations this way, you effectively reduce a system of equations into a simpler, single-variable equation.
This method is particularly useful because it transforms a difficult problem into a series of simpler steps.
By focusing first on one variable and substituting it into the second equation, you progressively narrow down the possible solutions until you can find the exact values for both variables.

Solving linear equations is a fundamental skill in algebra. A linear equation is any equation that can be written in the form of ax + by = c, where a, b, and c are constants.
To solve a linear equation, the goal is to isolate the variable on one side of the equation.
Here's a simple approach to solve:

• Combine like terms on both sides of the equation.
• Use inverse operations to isolate the variable term (addition/subtraction).
• If the variable has a coefficient, divide both sides of the equation by that coefficient to solve for the variable.

In the context of the substitution method, once you've isolated one variable, you substitute this expression into the other equation.
This will give you a linear equation with a single variable, which can be solved to find the value of that variable.

The solution of a system of linear equations involves finding the values of the variables that satisfy both equations simultaneously. In simpler terms, you're finding the point where the two lines represented by the equations intersect.
To verify your solution, you should substitute the values of the variables back into the original equations.
Here’s a quick rundown using the given exercise:

• First, you solve one equation for one variable and substitute it into the second equation (Substitution Method).
• Next, simplify and solve this single-variable equation to find the value of the variable (like solving linear equations).
• After that, substitute this value back into the expression you found for the other variable.
• The values you get for both variables form the solution to your system of equations.

For the given problem, we found the solution as x = 3 and y = -4. This means the point (3, -4) satisfies both original equations, making it the solution to the system.