Question

solve using substitution
1) 6x + 2y = 0
4x + y = -1

2) 3x + 2y = -4
x + 2y = -8

3) 5x - 4y = 14
x - 2y = -2

4) x + 3y = -4
4x + 5y = 5

5) x + 3y = -5
2x - y = 18
just answers please im running outa time!

Answer 1

That's a lot of questions. I can help you with the first one, maybe second one but you will have to work on the others yourself.

Answer 2

okay how do i start it?

Answer 3

I am going to explain this as best I can. Try and follow me, if you have questions, please ask so I know you understand. Ok?

Answer 4

ok thank you!

Answer 5

So, the idea of substitution is to set something equal to something so that you can substitute it into another equation. Do you remember from a few chapters or pre-algebra, when you had something that looked like f(4) = x+5
and all you had to do was substitute \(4\) whenever you saw an "x"? So, f(4) when you had f(x) = x+5 \(\Rightarrow\) 4+5 = 9

Answer 6

Well, this is the same thing. Except, now you are using your algebra tricks to get something in ONLY terms of "x" \(or\) "y". So that you can substitute it into equation

Answer 7

yes i remember!

Answer 8

Let's start by givint them numbers.

(1). 6x + 2y = 0
(2). 4x + y=-1

Answer 9

sooo...

Answer 10

Now, rearrange (1). to get ONLY "x".

So you will subtract 6x to both sides
STEP 1:
6x-6x+2y=0-6x \(\Rightarrow\) 2y = -6x

STEP 2: divide by 2, to get "y" by itself
\(\large\frac{2}{2}y = \frac{-6}{2}x\) \(\Rightarrow\) y = -3x

Answer 11

so y=-3???

Answer 12

Now, you see how you have \(y = -3x\)?? Now, you can substitute your NEW (1), call it equation (1A) into equation (2).

Answer 13

It is like saying f(-3x) = 4x+y=-1
except you are substituting it for \(y\) because you have \(y = -3x\)

Answer 14

So you get \(4x-3x=-1\)

Answer 15

\(x=-1\)

Answer 16

so the answer to number 1 is x =-1?

Answer 17

NOW, you have solved for "x"
That means x = -1!

now, plug in your found "x" into equation (1). and solve for \(y\)!! and you're done!!

Answer 18

\(6(-1)+2y = 0\) solving for \(y\) you get \(-6+2y=0\) and then

Answer 19

\(2y=6\) and you get y = 3!

So your final answer is: \( x = -1\) and \(y = 3\)
OR
(-1, 3)

Answer 20

sweet thank you very much!

Answer 21

You can check if these are right by plugging in those values for any of the two equations for your given system!

For instance, if you plug in x = -1 and y = 3 for the first equation, check it out!

\(6(-1)+2(3) = 0\)

and \(0=0\) is a true statement. Therefore, x = -1 and y = 3 are your answers!

Answer 22

do you know any of the answers to the other ones tho?

Answer 23

Yes.

Answer 24

could i just have the answers now im running outa time to do this workshett!