Question

Evaluate each expression if \(x=-2\) and \(y=3\). \(-2 x+x y\)

Short answer

-2

Step-by-step solution

Identify and Substitute Values

First, identify the given values for the variables. Here, we are given that \(x=-2\) and \(y=3\). Now, substitute these values into the expression \(-2x + xy\).

Substitute and Simplify

Substitute \(x = -2\) and \(y = 3\) into the expression:\[-2(-2) + (-2)(3)\]

Evaluate the Multiplications

Evaluate the multiplications separately:\(-2(-2) = 4\)and\(-2)(3) = -6\)

Add the Results

Combine the results from Step 3:\[4 + (-6) = 4 - 6 = -2\]

Key concepts

Variable substitution

Variable substitution is an essential process in algebra that helps you simplify and solve expressions. You start by identifying the given values of the variables.
In our exercise, we have two variables: \(x\) and \(y\). We know that \(x = -2\) and \(y = 3\), so we replace these variables with their values in the expression. The original expression is \(-2x + xy\).
By substituting \(x = -2\) and \(y = 3\), we transform the expression into:
\[-2(-2) + (-2)(3)\]
This substitution allows us to move forward with evaluating the expression.

Expression simplification

Once variables are substituted, the next step is to simplify the expression.
For our exercise, after substituting \(x = -2\) and \(y = 3\), we get:
\[-2(-2) + (-2)(3)\]
Simplification involves making the expression easier to understand and solve. Here, we'll resolve the individual multiplications before combining the results.
This transforms complex expressions into a simpler, more manageable form.

Multiplication in algebra

Multiplication in algebra is just like basic arithmetic but with variables. Here’s how it works in our example:
We have the products \(-2(-2)\) and \((-2)(3)\).

• First, \(-2\) times \(-2\): Two negatives make a positive, so \(-2 \times -2 = 4\).
• Next, \(-2\) times \(3\): A negative times a positive gives a negative, so \(-2 \times 3 = -6\).

Understanding these rules of multiplication helps you easily evaluate each part of the expression.

Addition and subtraction in algebra

Finally, we need to perform addition and subtraction to combine our results.
From our multiplication steps, we have the numbers \(4\) and \(-6\).
To combine them, you proceed with addition and subtraction:
\[4 + (-6)\]
Adding a negative number is the same as subtracting its absolute value, so:
\[4 + (-6) = 4 - 6 = -2\]
This final result is the value of the original expression after evaluating all components.