Questions: Why are the equations (x+y-y=x) and (x-y+y=x) called identities? These equations are called identities because the variables can be replaced with any number, and after completing the operations, the result is the original number. I can test this by replacing the variables with numbers. If I replace (x) with 10 and (y) with 4, the resulting number sentence (10+4-4=10) is true. The other resulting number sentence (10-4+4=10) is also true.

Why are the equations (x+y-y=x) and (x-y+y=x) called identities? These equations are called identities because the variables can be replaced with any number, and after completing the operations, the result is the original number. I can test this by replacing the variables with numbers. If I replace (x) with 10 and (y) with 4, the resulting number sentence (10+4-4=10) is true. The other resulting number sentence (10-4+4=10) is also true.
Transcript text: 2. Why are the equations $x+y-y=x$ and $x-y+y=x$ called identities? These equations are called identities because the variables can be replaced with any number, and after completing the operations, the result is the original number. I can test this by replacing the variables with numbers. If I replace $x$ with 10 and $y$ with 4 , the resulting number sentence $10+4-4=10$ is true. The other resulting number sentence $10-4+4=10$ is also true.
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Solution

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Solution Steps

Step 1: Understanding the Equations

The equations given are \(x + y - y = x\) and \(x - y + y = x\). These are called identities because they hold true for any values of \(x\) and \(y\).

Step 2: Simplifying the First Equation

For the equation \(x + y - y = x\), simplify by canceling out \(y\) and \(-y\): \[ x + y - y = x \] \[ x = x \]

Step 3: Simplifying the Second Equation

For the equation \(x - y + y = x\), simplify by canceling out \(-y\) and \(y\): \[ x - y + y = x \] \[ x = x \]

Final Answer

The equations are called identities because they hold true for any values of \(x\) and \(y\).

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