Chapter 6.3, Problem 31PPE

To determine

To find:A system of linear equations that can be solved using elimination method.

Answer to Problem 31PPE

  $\begin{array}{l}3x+3y=27\mathrm{......}(i)\\ x-3y=-11\mathrm{......}(ii)\end{array}$

And its solution is $x=4,y=5$ .

Explanation of Solution

Given information: The concept of elimination method to solve a system of linear equations is known.

Concept used:In elimination method, if the sum of coefficients of one variable in both equations is zero, then this variable`s terms are eliminated and resulted equation is solved for remaining variable. Further, this obtained value is put in any of the equation to get the value of the eliminated variable,

Calculation:Let the system of linear equations is,

  $\begin{array}{l}3x+3y=27\mathrm{......}(i)\\ x-3y=-11\mathrm{......}(ii)\end{array}$

Add both equations to eliminate y terms,

  $\begin{array}{l}3x+3y+x-3y=27-11\\ \Rightarrow 4x=16\\ \Rightarrow x=\frac{16}{4}=4\end{array}$

Plug in this value of x in second equation and solve for y as,

  $\begin{array}{l}4-3y=-11\\ \Rightarrow -3y=-11-5=-15\\ \Rightarrow y=\frac{15}{3}=5\end{array}$

Conclusion: So, on solving said system of linear equations $x=4,y=5$ , that is obtained by using elimination method.