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Any thoughts?

not really I'm so confused

Ok, they are using the method of substitution.

ok

That is where you solve for a variable and plug it into that variable in the other equation.

Both of these equations are already solved for y.

So, we can take what y= in one equation, and plug it in for y in the other equation.

|dw:1440003635482:dw|

i thought y = 4x

I'm not sure what you mean.

in equation b

or is that just the slope formula

Equation b is close to the slope formula, y=mx+b, but it has an x instead of y.

ok

But have you followed what I have said so far?

yes

So, if you plug in x+1 for y in the second equation, what do you get?

y=4x+6?

Hm, no, if we are subbing x+1 in for y, then we don't have y anymore.|dw:1440004062537:dw|

oh

:-) Does that make sense?

yep

Cool, so what is the answer?

Yep!

can u do another plz?

;)

Sure

Ok, well, let's see what happens if we do the same thing as the last problem.

What do you get when you sub 6x+9 for y in the second equation?

6x+9=6x+2?

Sweet! Can you simplify that?

combine like terms?

12x+9=+2??

No, to move one 6x to the other side, we need to subtract it

|dw:1440004496684:dw|

ohhhh i get it

so theres only one solution?

Sweet! So, any thoughts of what that tells us?

Hm, no. When the two equations simplify to a false statement (9 does not equal 2),

That means no solution

ohh

We can graph them to show that too.

They have the same slope, but different y intercepts

So they are parallel lines, and will never cross.

The solution is the point where the two lines cross.

one more??

Sure :-)

Ok, any thoughts?

no

The first equation is solved for y.

So, we take what y is in terms of x, and plug it into the other equation.

Can you try to do that?

im lost, ugh and my online teacher keeps reminding me about time crunch lol

|dw:1440004939079:dw| Aw, that's frustrating!

i see

It is like the other ones, just the second equation isn't solved for y.

ho do i slove

how

We aren't supposed to solve, just substitute.

ok

|dw:1440005055460:dw|

See how I subbed the 3x+4 in for y in the second equation?

yes

That is all we have to do :-)

Which answer does that look like?

Right

one more, last one i promise lol

Haha, ok

d + e = 15
âˆ’d + e = âˆ’5
Label the ordered pair as (d, e).
(0, 0)
(10, âˆ’5)
(5, 10)
(10, 5)

Ok, this one we actually do have to solve. Any thoughts on how to start?

not really

Well, what happens when we add the two equations together?

we sub?

We could, but we would have to solve for one of the variables first.

ok

I would suggest to use elimination on this one. It is the easier method. :-)

ok

|dw:1440005374033:dw| What happens when we add the two equations together?

im not sure

Just take a guess

elimintion

Ok, but what equation are we left with?

i honestly don't know

|dw:1440005536799:dw| See how I added the equations together?

yes

Can you combine like terms?

ill be back in one min, my teacher is calling me

I'm back @JoannaBlackwelder

Ok, can you combine like terms?

that one is kinda hard

It is a little different. d-d is what?

No, it is like 2-2.

Right. :-)

And e+e is what?

Close, 2e

oh i see

:-) And what is 15-5?

10

|dw:1440006758146:dw| Great!

See how I simplified that?

yep

Sweet, so we need to finish getting e by itself.

It is currently multiplied by 2

So, we need to divide the left side by 2 to leave just e (or 1e)

|dw:1440006877761:dw|

Good effort! But we need to divide by 2 to get e by itself, not 10

ok

|dw:1440006917075:dw|

ok

so whats my second point

Well, now that we know that e is 5, which answers do we have to choose from?

c,d

Are you sure that both c and d have e being 5?

c?

No, c, has e as 10.

thank u

You're welcome