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The substitution method is a key technique used in solving algebraic expressions by directly replacing variables with given numeric values. This method simplifies the process by turning a problem with variables into a numerical expression. In the context of our exercise, we're given variables \(x\), \(y\), and \(z\) with specified values: \(x = -2\), \(y = 7\), and \(z = -3\). By substituting these values into our expression \(2xy + 5xz\), we replace every occurrence of \(x\) with \(-2\), every \(y\) with \(7\), and every \(z\) with \(-3\). This transforms the abstract expression into a more tangible form that we can evaluate by performing arithmetic operations.
To perform this substitution:

• Substitute \(x = -2\), \(y = 7\), and \(z = -3\) into the expression \(2xy + 5xz\).

This leads us to the equation: \[ 2(-2)(7) + 5(-2)(-3) \] After substitution, the problem of finding the value of the original expression becomes a straightforward arithmetic task, paving the way for the next step in solving the problem.

Once substitution is done, the next step is evaluating the expression. Evaluating means simplifying the expression step by step until you find a numeric result. After substituting the given values, we have: \[ 2(-2)(7) + 5(-2)(-3) \] Start by tackling the multiplications, which is crucial in finding the final result. Each multiplication within the expression should be addressed with care:

• Calculate \(2(-2)(7)\) which results in \((-4)(7)\).
• Calculate \(5(-2)(-3)\) which results in \((-10)(-3)\).

The expression now looks like:\[ (-4)(7) + (-10)(-3) \] Simplifying further yields:

• The product \((-4)(7)\) equals \(-28\).
• The product \((-10)(-3)\) equals \(30\), since a negative times a negative gives a positive.

Finally, we add \(-28\) and \(30\) to complete the evaluation, giving us the result \(2\).
This final step confirms that the original algebraic expression evaluates to a simple number, providing an endpoint to our calculations.

Solving problems involving algebraic expressions requires a clear path and understanding of each step. The process can be outlined as follows:

• Understand the Problem: Familiarize yourself with the given algebraic expression and understand what is required. Replace variables with given values to convert the expression into a numeric format.
• Apply the Substitution Method: Substitute all given values into the expression to eliminate variables. This makes the expression easier to work with.
• Evaluate the Expression: Carry out multiplications and follow the arithmetic operations step by step, simplifying the expression progressively.
• Check and Interpret the Result: Once you have your final numeric value, it’s vital to review and ensure that all calculations are correct, ensuring logic follows from the original problem.

By following these structured steps, you develop a methodical approach to tackling algebraic problems. This strategy not only helps in solving the current problem but also equips you for handling similar problems in the future.