Chapter 6.3, Problem 4CB

To determine

To solve: given system of equations using elimination method.

Answer to Problem 4CB

  $x=5,y=-2$

Explanation of Solution

Given information: a system of equations is given as follows-

  $\begin{array}{l}3x+2y=11\\ 4x+y=18\end{array}$

Let

  $\begin{array}{l}3x+2y=11\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. (1)}\\ 4x+y=18\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{.(2)}\end{array}$

Multiplying equation (2) by 2 and subtracting from (1) we get,

  $\begin{array}{l}3x+2y-8x-2y=11-36\\ \Rightarrow -5x=-25\\ \Rightarrow x=\frac{-25}{-5}=5\end{array}$

Putting $x=5$ in equation (1) we get,

  $\begin{array}{l}3\times 5+2y=11\\ \Rightarrow 2y=11-15\\ \Rightarrow 2y=-4\end{array}$

  $\Rightarrow y=\frac{-4}{2}=-2$

Thus the required solution is $x=5,y=-2$

The main objective of elimination method is to eliminate the variable by adding or subtracting the two equations.

And we also eliminate variable in the above example by bringing 0 in the main diagonal and to.

But we eliminate only one type of variable in elimination method, and in above example we have eliminated both variables.