Question

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?

Answer 1

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)

`color(white)(xxxxxxx)3xcolor(red)(-y) = 5` .........................A
`color(white)(xxxxxxx)2xcolor(red)(+3y) = 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 xx3 rarr: color(white)(xx)9xcolor(red)(-3y) = 15` .......................C
`color(white)(xxxx.xxxxx)2xcolor(red)(+3y) = 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 rarr: color(white)(xxx)11x=25`

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