# A student is using the elimination method to solve the system of equations 3x-y=5, 2x+3y=10. What is the best first step method?

Nov 19, 2016

Multiply the first equation 3 so you create additive inverses with the y-terms.

#### Explanation:

The very BEST scenario you can have if you are using the elimination method is to have one of the variables being additive inverses. (same number but opposite signs)

$\textcolor{w h i t e}{\times \times \times x} 3 x \textcolor{red}{- y} = 5$ .........................A
$\textcolor{w h i t e}{\times \times \times x} 2 x \textcolor{red}{+ 3 y} = 10$ .......................B

In these two equations, note that the y-terms have opposite signs, but the numbers are different.

However, by multiplying equation A by 3, we will have additive inverses

$A \times 3 \rightarrow : \textcolor{w h i t e}{\times} 9 x \textcolor{red}{- 3 y} = 15$ .......................C
$\textcolor{w h i t e}{\times \times . \times \times x} 2 x \textcolor{red}{+ 3 y} = 10$ .......................B

Adding these two equations will cause the y-terms to add to 0, leaving only x terms, which can be solved.

$C + B \rightarrow : \textcolor{w h i t e}{\times x} 11 x = 25$

So the BEST first step would be to make additive inverses by multiplying equation by 3.