91Ó°ÊÓ

When solving linear equations, one of the fundamental steps is to isolate the variable we are solving for. In this exercise, we want to solve for the variable 'y' in the equation \( x - y = -3 \).
Isolating a variable means getting that variable all by itself on one side of the equation.
To do this, we use different algebraic operations to move other terms to the opposite side of the equation.
For instance, in the equation \( x - y = -3 \), we aim to isolate 'y' by moving 'x' to the other side.
This operation simplifies our equation and makes it possible to solve for 'y'.
Remember, keeping the equation balanced is key. Whatever operation we do on one side must also be done on the other.

The addition property of equality helps us keep an equation balanced when isolating variables.
This property states that we can add the same number to both sides of the equation without changing its solutions.
For example, in the equation \( x - y = -3 \), our first goal is to isolate 'y'.
We add 'y' to both sides:
\ [ x - y + y = -3 + y \ ]
This simplifies to: \ [ x = -3 + y \ ]
Notice how adding 'y' to both sides canceled out the -y on the left side, moving 'y' to the right side without changing the equality.

The subtraction property of equality is another vital tool when solving equations.
This property allows us to subtract the same number from both sides of the equation, maintaining its balance.
Continuing from the simplified equation we obtained, \( x = -3 + y \), we need to isolate 'y' by eliminating the -3 term.
We subtract -3 from both sides:
\ [ x + 3 = y \ ]
This final operation leaves us with the solution where 'y' is isolated: \ [ y = x + 3 \ ]
By using both the addition and subtraction properties of equality, we've successfully isolated 'y' and found the solution to the equation.