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In equations, isolating the variable you want to solve for is important because it makes it easier to find its value. Let's focus on isolating variable x in the given exercise.
To start, look at the original equation: \[A x + B y = C\] You want to get x by itself on one side of the equation. Begin by subtracting the term involving y (By) from both sides of the equation.
This gives you \[A x = C - B y\] It’s a crucial step because you now have an equation where that only has x without any other variables. Next, to make x completely alone, you divide everything by A.Now the equation is: \[ x = \frac{C - B y}{A} \] You’ve successfully isolated x by doing basic operations step by step.
This method helps simplify and solve equations one step at a time.

Linear equations are polynomials of the first degree, meaning they include terms with variables raised to the power of one. For example, the equation \[A x + B y = C\] is a linear equation because all the variables are to the first power.
Characteristics of linear equations include:

• They graph as straight lines.
• They have the form \[Ax + By + Cz + ... = D\]
• They can be solved using similar methods like addition, subtraction, multiplication, and division.

In the exercise, we are dealing with: \[Ax + By = C\] This means the solution will involve basic operations to rearrange the equation into simpler terms. Solving a linear equation often involves isolating a variable and then simplifying, as we did step by step.
Remember, understanding how linear equations work helps in manipulating and solving them efficiently.

Rearranging formulas involves changing the structure of an equation to solve for a different variable. This is useful in many areas of math and science.
In the exercise, we rearranged \[A x + B y = C \] to solve for x. The steps included:

• Subtracting \[B y\] from both sides
• Dividing by A

Rearranging a formula isn't just limited to linear equations. It can be applied to any type of equation where you need to solve for a different component.
The key techniques used in rearranging formulas include:

• Transpose terms: Move terms from one side to another by using addition or subtraction.
• Isolate the variable: Get the desired variable by itself using multiplication or division.

By understanding these steps and why we do them, you can apply these methods to a wide range of problems, not just the one in the exercise.