Chapter 3.1, Problem 37PPS

To determine

To write: Whether the equation $\frac{x}{2}=10+\frac{2y}{3}$ is a linear equation.

Answer to Problem 37PPS

The required answer is: Yes, it is a linear equation and its standard form is $3x-4y=60$

Explanation of Solution

Given information:

The given equation: $\frac{x}{2}=10+\frac{2y}{3}$

Calculation:

Rewrite the equation so that it appears in standard form $Ax+By=C$

  $\begin{array}{l}\frac{x}{2}=10+\frac{2y}{3}\\ \frac{x}{2}\times 2=(10+\frac{2y}{3})\times 2\end{array}$

(Multiplying 2 on both sides)

  $x=(10\times 2)+(\frac{2y}{3}\times 2)$

(Simplify)

  $\begin{array}{l}x=20+\frac{4y}{3}\\ x-20=20+\frac{4y}{3}-20\end{array}$

(Subtracting 20 from both sides)

  $\begin{array}{l}x-20=\frac{4y}{3}\\ (x-20)\times 3=\frac{4y}{3}\times 3\end{array}$

(Multiplying 3 on both sides)

  $\begin{array}{l}3x-60=4y\\ 3x-60-4y=4y-4y\end{array}$

(Subtracting 4y from both sides)

  $\begin{array}{l}3x-60-4y=0\\ 3x-60-4y+60=0+60\end{array}$

(Adding 60 to both sides)

  $3x-4y=60$

(Simplify)

The equation is now in standard form where $A=3,B=-4$ and $C=60$ .

Therefore, yes the given equation is a linear equation.

The standard form is $3x-4y=60$