Chapter 6, Problem 18GR

To determine

To determine elimination method to add or delete a variable from a system of equation.

Explanation of Solution

Given:

Elimination method to add or delete a variable from a system of equation

Concept used:

Elimination method to add or delete a variable

When the coefficients in a system having one variable opposing adding the equations to eliminate the variable.

For example, consider 2 equations:

  $\Rightarrow 2y+5x=10$

  $\Rightarrow 7y-5x=2$

Adding the equations to eliminate the variable,

  $\begin{array}{l}2y+5x=10\\ +7y-5x=2\\ \_\_\_\_\_\_\_\_\_\_\_\_\\ 9y+0x=12\end{array}$

Here, $x$ is eliminated.

So, $y=\frac{4}{3}$

When the coefficients of one variable are equal subtracting the equations to eliminate a variable.

  $\Rightarrow 2y+5x=10$

  $\Rightarrow 7y+5x=2$

Adding the equations to eliminate the variable,

  $\begin{array}{l}2y+5x=10\\ -7y+5x=2\\ \_\_\_\_\_\_\_\_\_\_\_\_\\ -5y+0x=8\end{array}$

Here $x$ is eliminated

So, $y=-\frac{8}{5}$

Conclusion:

Therefore, from the above example elimination method to add or delete a variable from a system of equation can be done.