Chapter 6.2, Problem 35PPE

To determine

To find: Theerror in given solution of system of linear equation and correct it.

Answer to Problem 35PPE

Step 2 in correct and system of equation will have exactly one solution.

Explanation of Solution

Given information:

The equations $7x+5y=14$ and $x+8y=21$ are solved as follows:

  

The step 1 of the solution process is correct as it correctly finds the value of x in terms of y from equation $x+8y=21$ .

However the step 2 of the solution is completely wrong. Since in order to further solve the equation the value of x obtained from step should be put in equation $7x+5y=14$ and not in equation $x+8y=21$ .

The correct step 2 will be as follows:

  $\begin{array}{c}7x+5y=14\\ 7\left(21-8y\right)+5y=14\\ 147-56y+5y=14\\ 147-51y=14\\ -51y=14-147\\ -51y=-133\\ y=\frac{133}{51}\end{array}$

Since a valid value of y is obtained, thus the system of equation will have exactly one solution.