PLZ HELP
Equation A: y = x + 1
Equation B: y = 4x + 5
Which of the following steps can be used to find the solution to the set of equations?
x + 1 = 4x + 5
x = 4x + 5
x + 1 = 4x
x + 5 = 4x + 1

- anonymous

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- anonymous

@JoannaBlackwelder

- JoannaBlackwelder

Any thoughts?

- anonymous

not really I'm so confused

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## More answers

- JoannaBlackwelder

Ok, they are using the method of substitution.

- anonymous

ok

- JoannaBlackwelder

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

- JoannaBlackwelder

Both of these equations are already solved for y.

- JoannaBlackwelder

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

- JoannaBlackwelder

|dw:1440003635482:dw|

- anonymous

i thought y = 4x

- JoannaBlackwelder

I'm not sure what you mean.

- anonymous

in equation b

- anonymous

or is that just the slope formula

- JoannaBlackwelder

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

- anonymous

ok

- JoannaBlackwelder

But have you followed what I have said so far?

- anonymous

yes

- JoannaBlackwelder

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

- anonymous

y=4x+6?

- JoannaBlackwelder

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

- anonymous

oh

- JoannaBlackwelder

:-) Does that make sense?

- anonymous

yep

- JoannaBlackwelder

Cool, so what is the answer?

- anonymous

a

- JoannaBlackwelder

Yep!

- anonymous

can u do another plz?

- anonymous

;)

- JoannaBlackwelder

Sure

- anonymous

Equation C: y = 6x + 9
Equation D: y = 6x + 2
Which of the following options is true about the solution to the given set of equations?
One solution
No solution
Two solutions
Infinite solutions

- JoannaBlackwelder

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

- JoannaBlackwelder

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

- anonymous

6x+9=6x+2?

- JoannaBlackwelder

Sweet! Can you simplify that?

- anonymous

combine like terms?

- JoannaBlackwelder

Yep

- anonymous

12x+9=+2??

- anonymous

@JoannaBlackwelder

- JoannaBlackwelder

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

- JoannaBlackwelder

|dw:1440004496684:dw|

- anonymous

ohhhh i get it

- anonymous

so theres only one solution?

- JoannaBlackwelder

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

- JoannaBlackwelder

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

- JoannaBlackwelder

That means no solution

- anonymous

ohh

- JoannaBlackwelder

We can graph them to show that too.

- JoannaBlackwelder

They have the same slope, but different y intercepts

- JoannaBlackwelder

So they are parallel lines, and will never cross.

- JoannaBlackwelder

The solution is the point where the two lines cross.

- anonymous

one more??

- JoannaBlackwelder

Sure :-)

- anonymous

y = 3x + 4
2x + 3y = 10
Which of the following steps could be used to solve by substitution?
3x + 4 = 2x + 3y
2x + 3(3x + 4) = 10
2(3x + 4) + 3y = 10
3(y = 3x + 4)

- JoannaBlackwelder

Ok, any thoughts?

- anonymous

no

- JoannaBlackwelder

The first equation is solved for y.

- JoannaBlackwelder

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

- JoannaBlackwelder

Can you try to do that?

- anonymous

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

- JoannaBlackwelder

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

- anonymous

i see

- JoannaBlackwelder

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

- anonymous

ho do i slove

- anonymous

how

- JoannaBlackwelder

We aren't supposed to solve, just substitute.

- anonymous

ok

- JoannaBlackwelder

|dw:1440005055460:dw|

- JoannaBlackwelder

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

- anonymous

yes

- JoannaBlackwelder

That is all we have to do :-)

- JoannaBlackwelder

Which answer does that look like?

- anonymous

b

- JoannaBlackwelder

Right

- anonymous

one more, last one i promise lol

- JoannaBlackwelder

Haha, ok

- anonymous

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

- JoannaBlackwelder

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

- anonymous

not really

- JoannaBlackwelder

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

- anonymous

we sub?

- JoannaBlackwelder

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

- anonymous

ok

- JoannaBlackwelder

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

- anonymous

ok

- JoannaBlackwelder

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

- anonymous

im not sure

- JoannaBlackwelder

Just take a guess

- anonymous

elimintion

- JoannaBlackwelder

Ok, but what equation are we left with?

- anonymous

i honestly don't know

- JoannaBlackwelder

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

- anonymous

yes

- JoannaBlackwelder

Can you combine like terms?

- anonymous

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

- JoannaBlackwelder

Ok

- anonymous

I'm back @JoannaBlackwelder

- JoannaBlackwelder

Ok, can you combine like terms?

- anonymous

that one is kinda hard

- JoannaBlackwelder

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

- anonymous

d

- JoannaBlackwelder

No, it is like 2-2.

- anonymous

0

- JoannaBlackwelder

Right. :-)

- JoannaBlackwelder

And e+e is what?

- anonymous

e

- JoannaBlackwelder

No, we add the coefficients, and when there is no coefficient written it is understood to be 1. So this is 1e+1e

- anonymous

2

- JoannaBlackwelder

Close, 2e

- anonymous

oh i see

- JoannaBlackwelder

:-) And what is 15-5?

- anonymous

10

- JoannaBlackwelder

|dw:1440006758146:dw| Great!

- JoannaBlackwelder

See how I simplified that?

- anonymous

yep

- JoannaBlackwelder

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

- JoannaBlackwelder

It is currently multiplied by 2

- JoannaBlackwelder

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

- anonymous

|dw:1440006877761:dw|

- JoannaBlackwelder

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

- anonymous

ok

- JoannaBlackwelder

|dw:1440006917075:dw|

- anonymous

ok

- anonymous

so whats my second point

- JoannaBlackwelder

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

- anonymous

c,d

- anonymous

?

- JoannaBlackwelder

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

- anonymous

c?

- JoannaBlackwelder

No, c, has e as 10.

- anonymous

d

- JoannaBlackwelder

Yep, that is the only answer that has e as 5. We would normally also have to find d, but they gave us a shortcut. :-)

- anonymous

thank u

- JoannaBlackwelder

You're welcome

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