Q62. - Algebra 2

Question

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

$3x=2-5y$

Step-by-Step Solution

Answer

The standard form of the equation is $3x+5y=2$ and $A=3, B=5, C=2$.

Step-1 – Apply the concept of Standard form of equation

Any linear equation with variables x and y can be expressed in the standard form as:

$Ax+By=C$

Where A, B, and C are all integers with greatest common factor as 1.

Step-2 – Convert the equation into standard form

Consider the given equation.

$3x=2-5y$

To convert it into standard form, add 5y on both sides of equation.

$\begin{array}{c}3x+5y=2-5y+5y\\ 3x+5y=2\end{array}$

Thus, the standard form of the equation is $3x+5y=2$.

Step-3 – Identification of A, B, and C

Comparing $3x+5y=2$ with standard form $Ax+By=C$, we get

$\begin{array}{l}A=3\\ B=5\\ C=2\end{array}$

Hence, the standard form of the equation is $3x+5y=2$ and $A=3, B=5, C=2$.