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

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

Solution

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: \[ 4x - 4y \]