Question

Medal for extreme help :) Thank You !!
PART 1-When solving systems of equations, how do you determine what method to use?

PART 2- Choose 1 system of equations from the choices below. Then, solve the system and post your solution, showing your steps of the method you chose.


• –y + 3x = 6
y = –6x + 12



• 6x – 4y = 54
–9x + 2y = –69



• 2y = x + 1
–2x – y = 7

Answer 1

I'm not too good at explaining this, I think.
But, in my opinion, the easiest method to solving a system of equations is by elimination.

One way to do this is to multiply one the equations by some constant.
So, when you add the two equations, one of the variables will cancel out.

-y + 3x = 6
-y = -6x + 12

Rearrange the terms so the similar terms are on the same side.

-y + 3x = 6
-y + 6x = 12 <-- I added 6x on both sides.

Elimination is good to use here. We can easily cancel out the x terms by addition. But first, we must multiply the top equation by -2.

-2 - 6x = -12
-y + 6x = 12

I multiplied by -2 because I know I needed the 3x to somehow cancel with 6x.
I can turn 3x into -6x by multiplying it by -2.

Add the two equations: -3y = 0
Solve for y: y = 0

Plug 'y' back into one of the equations. Preferably, use the equation you didn't change.
-y + 6x = 12
0 + 6x = 12 -> Divide both sides by 6
x = 2

(2,0) is the solution to this system.

Answer 2

Whoops, I wanna clear up some math in the middle.
Elimination is good to use here. We can easily cancel out the x terms by addition. But first, we must multiply the top equation by -2.

2y - 6x = -12
-y + 6x = 12

I multiplied by -2 because I know I needed the 3x to somehow cancel with 6x.
I can turn 3x into -6x by multiplying it by -2.

Add the two equations: y = 0
Solve for y: y = 0

Answer 3

ty

Answer 4

The goal is to choose the method that results in the least amount of steps.