Chapter 3.1, Problem 1CYU

To determine

Determine the equation $x=y-5$ is a linear equation or not. Write in Standard form.

Answer to Problem 1CYU

Yes, this is a linear equation.

Standard form: $\text{x}-\text{y + 5 = 0 }$

Explanation of Solution

Given:

The equation: $x=y-5$

Concept Used:

A linear equation is any equation that can be written in the form. $ax+b=0$ . Where a and b are real numbers and x is a variable. This form is sometimes called the standard form of a linear equation.

No variable in a linear equation is raised to a power greater than 1. Linear equations are those equations that are of the first order.

Standard form of Linear Equation is $\text{A}x+\text{B}y+\text{C}\text{=}\text{0}$ , where A , B and C are any integer.

Calculation:

The equation: $x=y-5$

Rewrite the equation in standard form.

  $\begin{array}{l}\text{x}=\text{y}-5\\ \text{x}-\text{y}=\text{y}-\text{y}-5\text{[}\text{Subtract}y\text{to}\text{both}\text{sides}\text{]}\\ \text{x}-\text{y = }-\text{5}\\ \text{x}-\text{y}\text{+5}\text{=}-\text{5}\text{+5 [}\text{Add}5\text{to}\text{both}\text{sides}\text{]}\\ \text{x}-\text{y +5 = 0 }\end{array}$

The equation is now in standard form where A = 1, B = − 1 and C = 5.

This is a linear equation.

Thus, this is a linear equation. Standard form: $\text{x}-\text{y + 5 = 0 }$