Q1. CYU - Algebra 1

Question

Determine whether each equation is a linear equation. Write yes or no. If yes, write the equation in standard form.

$x=y-5$

Step-by-Step Solution

Answer

Yes, the given equation $x=y-5$ is a linear equation and the given equation $x=y-5$ in standard form is $x-y=-5$.

Step 1. Determine whether the given equation is a linear equation.

A linear equation is an equation that forms a line when it is graphed. Linear equations are written in the form $Ax+By=C$, where A and B are not both zero and A, B and C are integers with greatest common factor of 1.

 

The given equation is $x=y-5$.

 

The given equation can be written as:

$$\begin{gathered} x=y-5 \\ x-y=-5 \end{gathered}$$ 

Therefore, by comparing the given equation $x-y=-5$ with the equation $Ax+By=C$, it can be noticed that:

 

$A=1, B=-1$ and $C=-5$.

 

As, the equation $x=y-5$ can be written in the form $Ax+By=C$.

 

Therefore, yes, the given equation $x=y-5$ is a linear equation.

Step 2. Write the given equation in standard form.

The given equation is $x=y-5$.

 

The standard form of the linear equation is $Ax+By=C$.

 

The given equation in standard form is:

$x-y=-5$

 

Where, $A=1, B=-1$ and $C=-5$.