Question

Solve 2x – 2y = 5 for y.

Answer 1

`\large\boxed{\tt y = x - 2.5}`

Explanation:

`\textsf{We are asked to solve for the value of y.}`

`\textsf{Because there's 2 variables, and just a whole number on the right side of the}`

`\textsf{equation, it's impossible to find the exact value of y. For finding y, it has to involve}`

`\textsf{using the rest of the values where we subtract the right side of the equation by}`

`\textsf{the left side, excluding the variable we are trying to find. This is called \underline{Isolation}.}`

`\large\underline{\textsf{What is Isolation?}}`

`\textsf{Isolation in Mathematics is isolating a certain term to find the value of what's asked.}`

`\textsf{Isolation is commonly used to find variables, where we use the \underline{Properties of Equality}}`

`\textsf{to find what's missing.}`

`\large\underline{\textsf{What are the Properties of Equality?}}`

`\textsf{Properties of Equality are properties that allow us to manipulate one side of the}`

`\textsf{equation, which we have to do the same for the other side which says both expressions}`

`\textsf{are equal to each other.}`

`\large\underline{\textsf{Solving;}}`

`\textsf{We will Isolate y by using the \underline{Properties of Equality.}}`

`\tt 2x-2y=5`

`\textsf{To isolate y, we should use the \underline{Subtraction Property of Equality} where we subtract}`

`\textsf{the same term from both sides of the equation, which states that both expressions}`

`\textsf{will still be equal to each other.}`

`\underline{\textsf{Subtract 2x from both sides of the equation;}}`

`\tt 2x-2x-2y=-2x+5`

`\tt -2y = -2x+5`

`\textsf{Remember that we are asked for the value of y, which means that y shouldn't have}`

`\textsf{any coefficients. We want to remove that coefficient by using the \underline{Division Property}}`

`\textsf{\underline{of Equality} to divide both sides of the equation by -2.}`

`\underline{\textsf{Divide both sides of the equation by -2;}}`

`\tt (-2y)/(-2) = (-2x+5)/(-2)`

`\large\boxed{\tt y = x - 2.5}`

Answer 2

Hi!

To solve this for y, we want to isolate the y variable on one side of the equation.

Given:

`2x-2y=5`

Add 2y to both sides:

`2x=5+2y`

Subtract both sides by 5:

`2x-5=2y`

Divide both sides by 2:

`(2x-5)/(2) =y`