Question

5x-y=-9
x-y=-1 can anyone help me solve this equation.
here are my choices for this question. (1,2) (2,1)
(-1,-2) (-2,-1)

Answer 1

Looks like a system of equations that can be solved by elimination or substitution.

Answer 2

can u help me with this problem

Answer 3

Only if you are willing to show some effort.

Answer 4

yes i am

Answer 5

Do you have any idea how you might start to solve this?

Answer 6

honestly no first time doing this problem

Answer 7

OK.
Two options that I can help you with are:
Substitution - solve one equation for one variable and substitute that into the other equation.
Elimination - using addition or subtraction to eliminate one variable.
They are usually taught at two different methods but I see them as variations on a theme.

Answer 8

Elimination might be the most efficient way to solve this system of equations.

Answer 9

\(5x-y=-9\)
\(x-y=-1 \)
The idea is to eliminate one of the variables. Any thoughts?

Answer 10

5x-y=-10??

Answer 11

I like the way you think, but it's not quite what I meant.
Remember that you can do anything you want to an equation as long as you do the same thing to every term in the equation.

Answer 12

Also remember that you can combine like terms.

Answer 13

ohhh... ok makes a little bit more sense

Answer 14

This will be a bit of the scenic route but I think it will help you to understand the process better.
Try adding the two equations together and see what you get.

Answer 15

how would i do that again

Answer 16

Combine like terms:
5x + x
-y + -y
-9 +-1
Keep them in the same columns

Answer 17

i dont get how i can set this up

Answer 18

5x -y = -9
x -y = -1
----------
6x -2y = -10

Answer 19

Do you see what I did?

Answer 20

i kinda did

Answer 21

do i sole that equation

Answer 22

No, I did warn you that this was the long way around.
You can do what ever you want to an equation as long as you do the same thing to each term in the equation.
Using what I just showed you about adding the equations, what can you do to one of the equations to eliminate one of the variables?

Answer 23

divide it by 2 o divide it by 6 on both sides

Answer 24

That will reduce a variable to a coefficient of 1.
5x-y=-9
x-y=-1
Look at only these equations and try again. When you add them together as I did, you want one of the variables to add to 0.

Answer 25

ohh ok

Answer 26

Do you know what you need to do?

Answer 27

no.. :(

Answer 28

You need to change one equation so that adding the coefficients together will equal 0.
Think additive inverse.

Answer 29

1-1 = 0
-4+4=0
...

Answer 30

Look at the y terms. What can you multiply by to give them opposite signs?

Answer 31

2

Answer 32

\(-y \times 2 = -2y\)

Answer 33

\(-y \times\) what? \(= 0\)

Answer 34

4y

Answer 35

-y + y = 0
Sorry, I was using the wrong operation. You want to add the equations so I should have said:
\(-y + \) what? \(=0\)

Answer 36

So, what can you multiply the -y by to change the sign to positive?