Chapter 7, Problem 36CR

To determine

To draw: The graph of lines in the system, then check system is consistent or inconsistent. If system is consistent determine solution.

Answer to Problem 36CR

The given system of equations is consistent. Solution is $x=-7.52,y=0.9$

Explanation of Solution

Given Information: Given a system of equations

  $-x+3.2y=10.4,-2x-9.6y=6.4$

The given set of equations $-x+3.2y=10.4,-2x-9.6y=6.4$ . Draw the graph of these equations.

  

It is seen that both the lines are intersecting.

This means given lines are intersecting.

Therefore, system has unique solution

System is consistent

Now solve the equation algebraically

  $-x+3.2y=10.4$ -----------------(i)

  $-2x-9.6y=6.4$ -----------------(ii)

Multiply (i) by 3 and add equation (ii)

  $-3x+9.6y=31.2$

  $-2x-9.6y=6.4$

  -----------------------

  $-5x$ = 37.6

  $x=\frac{-37.6}{5}=-7.52$

Put value of x in eq (i)

  $-(-7.52)+3.2y=10.4$

  $\begin{array}{l}7.52+3.2y=10.4\\ 3.2y=10.4-7.52\\ 3.2y=2.88\\ y=\frac{2.88}{3.2}\\ y=0.9\end{array}$