Questions: Combine Like Terms: -x+5x+y-5y

Combine Like Terms: -x+5x+y-5y
Transcript text: Combine Like Terms: $-x+5 x+y-5 y$
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Solution

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Solution Steps

To combine like terms, we need to group the terms with the same variable together and then sum their coefficients. In this case, we have terms with \(x\) and terms with \(y\). We will sum the coefficients of \(x\) and \(y\) separately.

Step 1: Identify and Group Like Terms

We start by identifying and grouping the like terms in the expression \(-x + 5x + y - 5y\). The terms with \(x\) are \(-x\) and \(5x\), and the terms with \(y\) are \(y\) and \(-5y\).

Step 2: Sum the Coefficients of Like Terms

Next, we sum the coefficients of the like terms:

  • For \(x\): The coefficients are \(-1\) and \(5\). Summing these gives: \[ -1 + 5 = 4 \]
  • For \(y\): The coefficients are \(1\) and \(-5\). Summing these gives: \[ 1 - 5 = -4 \]
Step 3: Form the Simplified Expression

Using the summed coefficients, we form the simplified expression: \[ 4x - 4y \]

Final Answer

\[ \boxed{4x - 4y} \]

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