Chapter ISG, Problem 6.4.4P

To determine

To solve the system of equations

Answer to Problem 6.4.4P

  $m=-2$ and $n=5$ are the solution

Explanation of Solution

Given information:

  $\begin{array}{l}-m+3n=17\\ 4m-6n=-38\end{array}$

Calculation:

Lets assume the equation be (1) and (2) respectively

To solve equations by elimination, the given equations are either added or subtracted to get an equation in only one variable.

Let’s eliminate variable n here. To eliminate a variable, the coefficients of the variable must be same in both the equations.

In equation 1, coefficient of n is 3& in equation 2, coefficient of n is 6. To make the coefficients same, lets multiply equation 1 with 2.

  $2(-m+3n)=17\times 2$

Solving,

  $-2m+6n=34$   (3)

Now, add (3) and (2)

  $4m-6n-2m+6n=-38+34$

Solving,

  $2m=-4$

Dividing by 2,

  $m=-2$

Putting value of m in (2),

  $-2(-2)+6n=34$

Solving,

  $4+6n=34$

So,

  $6n=30$

Dividing equation by 6,

  $n=5$

Hence, $m=-2$ and $n=5$ are the solution of the system