Chapter 11, Problem 5RE

To determine

To find: The solution of expression $\left\{\begin{array}{l}x-3y+4=0\\ \frac{1}{2}x-\frac{3}{2}y+\frac{4}{3}=0\end{array}\right\}$ .

Answer to Problem 5RE

The solution of the equation is inconsistent.

Explanation of Solution

Given information:

The given equation is $\left\{\begin{array}{l}x-3y+4=0\\ \frac{1}{2}x-\frac{3}{2}y+\frac{4}{3}=0\end{array}\right\}$

Calculation:

Calculate the expression,

  $\left\{\begin{array}{l}x-3y+4=0\\ \frac{1}{2}x-\frac{3}{2}y+\frac{4}{3}=0\end{array}\right\}$

Divide both sides of the equation $x-3y=-4$ by $-2$ so as to make the coefficients of $x$ negatives of one another.

  $-\frac{1}{2}x+\frac{3}{2}y=2$

Now the system of equation can be written as $\left\{\begin{array}{l}-\frac{1}{2}x+\frac{3}{2}y=2\\ \frac{1}{2}x-\frac{3}{2}y=-\frac{4}{3}\end{array}\right\}$

The coefficient of $x$ and $y$ in the system of equation are negatives of one another and thus cannot be solved.

Therefore, the solution of equation is inconsistent.