Chapter 6.2, Problem 33PFA

To determine

To find: Values of x and y .

Answer to Problem 33PFA

No solution

Explanation of Solution

Given information:

  $\begin{array}{l}3x+2y=-8\\ -6x-4y=12\end{array}$

Any system of equation in the form

  $\begin{array}{l}{a}_{1}x+b_{1}y+c_1=0\\ a_{2}x+b_{2}y+c_2=0\end{array}$

  $\begin{array}{l}3x+2y=-8\\ \Rightarrow 3x+2y+8=0\end{array}$

Is the first equation.

  $\begin{array}{l}-6x-4y=12\\ \Rightarrow -6x-4y-12=0\end{array}$

Is the second equation.

Here

  $\begin{array}{l}\frac{a_1}{a_2}=\frac{3}{-6}\\ \Rightarrow \frac{a_1}{a_2}=\frac{-1}{2}\end{array}$

  $\begin{array}{l}\frac{b_1}{b_2}=\frac{2}{-4}\\ \Rightarrow \frac{b_1}{b_2}=\frac{-1}{2}\end{array}$

  $\begin{array}{l}\frac{c_1}{c_2}=\frac{8}{-12}\\ \Rightarrow \frac{c_1}{c_2}=\frac{-2}{3}\end{array}$

Therefore

We got

  $\Rightarrow \frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$

As this is the required condition for no solution.

So there will be no solution.