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Chapter 15: Problem 55

Evaluate. \(y-x,\) for \(x=10\) and \(y=3\)

Short Answer

Expert verified
The result is -7.

Step by step solution

01

Understand the Problem

The problem requires evaluating the expression \(y - x\) given the values of \(x\) and \(y\).
02

Substitute Given Values

Substitute \(x = 10\) and \(y = 3\) into the expression \(y - x\).
03

Perform the Calculation

Calculate the result by subtracting the value of \(x\) from \(y\). Substitute into the expression: \[ y - x = 3 - 10 = -7 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

evaluating expressions
Evaluating expressions in algebra often requires understanding what each part of an expression means and then performing the necessary operations. Let's break down the expression in our example:

  • The expression we are working with is \( y - x \).
In this expression, \( y \) and \( x \) are variables, meaning their values are not fixed and can change.

To evaluate the expression, you need specific values for these variables. In this case, we are given \( x = 10 \) and \( y = 3 \).

Once we know the values, we can replace (or substitute) the variables in the expression with these numbers and then carry out the operations.
substitution method
The substitution method is a straightforward way to solve algebra problems by replacing variables with their actual values.

To use the substitution method:

  • Identify the values given for each variable.
  • Replace the variables in the expression with these values.
For our example:

\( y - x \)

We know \( y = 3 \) and \( x = 10 \). So, we substitute these values into the expression:

\[ y - x = 3 - 10 \]

After substitution, the expression contains only numbers, making it easier to evaluate using basic arithmetic.
basic arithmetic operations
Basic arithmetic operations are the foundation for all algebraic calculations. These include addition, subtraction, multiplication, and division. In our example, we are performing a subtraction.

Subtraction involves finding the difference between two numbers.

For our example, after substitution, our expression is:

\[ 3 - 10 \]

Here, we subtract 10 from 3:

\[ 3 - 10 = -7 \]

The result, \( -7 \), tells us the size of the gap between the numbers on a number line and its direction (left of zero).

Remember:
  • If you subtract a larger number from a smaller one, the result is negative.
  • If you subtract a smaller number from a larger one, the result is positive.

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Most popular questions from this chapter

Solve each system graphically. $$ \begin{aligned} &x-y=1\\\ &x+y=3 \end{aligned} $$

Find two numbers for which the sum is 108 and the difference is \(50 .\)

Solve each system using the substitution method. $$ \begin{aligned} &3 x+5 y=3\\\ &x=8-4 y \end{aligned} $$

Evaluate. The area of a parallelogram with base \(b\) and height \(h\) is \(b h\). Find the area of the parallelogram when the height is \(3.5 \mathrm{cm}\) and the base is \(8 \mathrm{cm} .\) (GRAPH CANT COPY)

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