Q2. CYU - Algebra 1

Question

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

$-2x-3=y$

Step-by-Step Solution

Answer

Yes, the given equation $-2x-3=y$ is a linear equation and the given equation $-2x-3=y$ in standard form is $2x+y=-3$.

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 $-2x-3=y$.

 

The given equation can be written as:

$$\begin{gathered} -2x-3=y \\ -3=2x+y \end{gathered}$$ 

Therefore, by comparing the given equation $2x+y=-3$ with the equation $Ax+By=C$, it can be noticed that:

 

$A=2, B=1$ and $C=-3$.

 

As, the equation $-2x-3=y$ can be written in the form $Ax+By=C$.

 

Therefore, yes, the given equation $-2x-3=y$ is a linear equation.

Step 2. Write the given equation in standard form.

The given equation is $-2x-3=y$.

 

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

 

The given equation in standard form is:

$2x+y=-3$

 

Where, $A=2, B=1$ and $C=-3$.