Q6. - Algebra 2

Question

Write each equation in standard form. Identify $A, B$ and $C$.

$y=3x-5$

Step-by-Step Solution

Answer

The required values are $A=3, B=-1, C=5$.

Step 1 – Standard form of a linear equation.

The standard form of a linear equation is $Ax+By=C$, where $A\ge 0, A$and $B$ are not both zero.

Step 2 – Rewrite the given linear equation in the standard form.

The given equation is:

$y=3x-5$

Subtract $3x$ from both sides.

$\begin{array}{l}y-3x=3x-5-3x\\ -\left(3x-y\right)=-5\end{array}$

Multiply both sides by -1 .

$\begin{array}{l}-\left(3x-y\right)\times \left(-1\right)=-5\times \left(-1\right)\\ 3x-y=5\end{array}$

Step 3 – Find the required values.

Now compare the equation $3x-y=5$ with the standard form of the linear equation $Ax+By=C$ to find the values of $A, B, C$.

$\begin{array}{l}A=3\\ B=-1\\ C=5\end{array}$

Thus, the required values are $A=3, B=-1, C=5$.