Given: The expressions below
![5x-9,13x-2y,7+x](https://img.qammunity.org/2023/formulas/mathematics/college/7ubtnqyb2ya9twh14rhj9en5xezok5ib0c.png)
To Determine: The variables, constants, coefficients, terms, and like terms
Solution
A variable is any entity that can take on different values
The variables are: x and y
![variables:x,y](https://img.qammunity.org/2023/formulas/mathematics/college/nx299sqglvh8w4lgnik93v3xk0jg4xrv68.png)
A constant does not change its value over time. A variable, on the other hand, changes its value dependent on the equation. Constants are usually written in numbers. Variables are specially written in letters or symbols
The constants are: -9, 7
![constants:-9,7](https://img.qammunity.org/2023/formulas/mathematics/college/2fh4k2vggfp8uiu9a86cq13g8bou3ws17y.png)
coefficients: A coefficient is a constant by which a variable is multiplied
![\begin{gathered} coefficients(x):5,13,1 \\ coefficients(y):-2 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/3lffleuhfcirb6icywtlul4q4qp9jeoq79.png)
Terms
A term is a single mathematical expression. It may be a single number (positive or negative), a single variable ( a letter ), several variables multiplied but never added or subtracted. Some terms contain variables with a number in front of them. The number in front of a term is called a coefficient
![Terms:5x,-9,13x,-2y,7,x](https://img.qammunity.org/2023/formulas/mathematics/college/r7kf4yrgeh9h8s7isgra3chc8308oqjfkt.png)
Like terms
Like terms are terms that have the same variables and powers. The coefficients do not need to match
![\begin{gathered} Like-terms: \\ (x-terms):5x,13x,x \\ (constant-terms):-9,7 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/5iz2njcco97v8kq05dae3g9zu462o6hq4x.png)
Answer Summary