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The substitution method is a powerful tool in solving linear equations. It involves substituting one variable with a given value or an expression to simplify the equation. Here, we'll use the substitution method to find the value of another variable.
For example, let's take the equation:\br>\(2x - 5y = 10\)\br>We are asked to find the value of \( y \) when \( x = -2 \) and \( x = 4 \).\br> In part (a), when \( x = -2 \) , we substitute \( -2 \) into the equation, making it:\br>\(2(-2) - 5y = 10\).\br> This simplifies to:\br>\(-4 - 5y = 10\).\br> Next, we solve for \( y \) , which is further simplified in the Isolating Variables section. These steps make solving more manageable and systematic.

Isolating variables means rearranging the equation so that the desired variable is on one side, making it easy to solve. Going back to our previous example where we had:\br> \(-4 - 5y = 10\)\br>First, add 4 to both sides to get:\br>\(-5y = 14\)\br>Next, divide both sides by \(-5\):\br>\( y = -\frac{14}{5}\) or \(-2.8\).\br>This gives us our result for part (a). Repeating similar steps for part (b) where \( x = 4 \):\br>Substitute \( 4 \) into the original equation:\br>\(2(4) - 5y = 10\)\br>which simplifies to:\br> \(8 - 5y = 10\).\br> Solving for \( y \) , we subtract 8 from both sides:\br> \(-5y = 2\)\br> Divide both sides by \( -5 \):\br>\( y = -\frac{2}{5} \) or \(-0.4\).\br>Isolating variables is crucial as it allows you to clearly view and solve for unknowns efficiently.

Basic Algebra is the foundation for solving linear equations and many other types of math problems. It involves understanding the relationships between numbers and variables, and how to manipulate them using operations such as addition, subtraction, multiplication, and division.
Let's review the initial problem: \(2x - 5y = 10\).\br> Mathematics allows us to solve for any variable by performing operations on both sides of the equation to maintain balance. Start by substituting known values into the variables, as shown in the Substitution Method.\br> Next, use techniques to isolate variables, exemplified in the Isolating Variables section. This includes performing inverse operations, like adding or subtracting terms, and multiplying or dividing by coefficients.\br> These foundational skills in Algebra not only help to solve linear equations but also provide a stepping stone to more complex topics in mathematics. Remember to practice these steps regularly to become more proficient and confident in handling algebraic expressions and equations.