Chapter 5.3, Problem 20E

To determine

To explain:

An error and correct it by solving the following linear system of equations:

  $\begin{array}{l}4x+3y=8\\ x-2y=-13\end{array}$

Answer to Problem 20E

The addition of two equations gives the value of variable $x$ , addition of $5x$ and $x$ should be $6x$ not $4x$ , which gives the wrong value for variable $x$ , so this is the error.

The correct solution of $\begin{array}{l}4x+3y=8\\ x-2y=-13\end{array}$ is $x,y=4,\frac{4}{7}$ .

Explanation of Solution

Given information:

  

  $\begin{array}{l}4x+3y=8\\ x-2y=-13\end{array}$

Calculation:

The given equations are as:

  $4x+3y=8$....................... (1)

  $x-2y=-13$....................... (2) From the given image of calculation:

The equation is multiplied by $-4$ , but on the right side of second equation value is not correct when its multiplied by $-4$ , it must be $52$ but it is multiplied by $-13$ , this is error for given calculation.

Now, the correct method of the elimination for given two eqns. is:

  $4x+3y=8$....................... (1)

  $x-2y=-13$$\times 4$

  $-4x+8y=52$....................... (2)

Take addition of equation (1) and (2) to eliminate variable $x$ :

  $\begin{array}{l}4x+3y-4x+8y=8+52\\ 11y=60\\ y=\frac{60}{11}\end{array}$

Now calculate the value of variable $x$ by putting value of $y=\frac{60}{11}$ in eq. (2):

  $\begin{array}{l}-4x+8y=52\\ -4x+8\left(\frac{60}{11}\right)=52\\ -44x+480=572\\ -44x=92\\ x=\end{array}$

Hence, by solving two equations by elimination method get variable values as $x,y=4,\frac{4}{7}$ .

Check for solution:

  $x,y=4,\frac{4}{7}$

Use eq. (2) as:

  $\begin{array}{l}x+7y=8\\ 4+7\left(\frac{4}{7}\right)=8\\ 8=8\end{array}$

Hence, verified.