Chapter 6.3, Problem 10P

$3x-5y=9$

Writing For the system $2x+y=3$

which variable should you eliminate first and why? How will you eliminate that variable?

To determine

To find: for the given system which variable should eliminate first and why and also process to eliminate.

Answer to Problem 10P

First eliminate variable y .

Explanation of Solution

Given information: the system of equation

  $\begin{array}{l}3x-5y=9\\ 2x+y=3\end{array}$

to find the which variable first eliminate solve both equations,

If operation subtraction or addition direct than no term cancel,

If multiply in $2x+y=3$ equation by 5, then it becomes $10x+5y=3$ ,

Now, add first equation and second equation,

  $\begin{array}{l}\underset{\_}{\begin{array}{l}10x+5y=3\\ 3x-5y=9\end{array}}\\ 13x+0y=12\\ 13y=12\\ y=\frac{12}{13}\end{array}$

Therefore first eliminate the variable y , then substitute y in anyone equation and find value of x .