anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
@JoannaBlackwelder
JoannaBlackwelder
  • JoannaBlackwelder
Any thoughts?
anonymous
  • anonymous
not really I'm so confused

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More answers

JoannaBlackwelder
  • JoannaBlackwelder
Ok, they are using the method of substitution.
anonymous
  • anonymous
ok
JoannaBlackwelder
  • JoannaBlackwelder
That is where you solve for a variable and plug it into that variable in the other equation.
JoannaBlackwelder
  • JoannaBlackwelder
Both of these equations are already solved for y.
JoannaBlackwelder
  • JoannaBlackwelder
So, we can take what y= in one equation, and plug it in for y in the other equation.
JoannaBlackwelder
  • JoannaBlackwelder
|dw:1440003635482:dw|
anonymous
  • anonymous
i thought y = 4x
JoannaBlackwelder
  • JoannaBlackwelder
I'm not sure what you mean.
anonymous
  • anonymous
in equation b
anonymous
  • anonymous
or is that just the slope formula
JoannaBlackwelder
  • JoannaBlackwelder
Equation b is close to the slope formula, y=mx+b, but it has an x instead of y.
anonymous
  • anonymous
ok
JoannaBlackwelder
  • JoannaBlackwelder
But have you followed what I have said so far?
anonymous
  • anonymous
yes
JoannaBlackwelder
  • JoannaBlackwelder
So, if you plug in x+1 for y in the second equation, what do you get?
anonymous
  • anonymous
y=4x+6?
JoannaBlackwelder
  • JoannaBlackwelder
Hm, no, if we are subbing x+1 in for y, then we don't have y anymore.|dw:1440004062537:dw|
anonymous
  • anonymous
oh
JoannaBlackwelder
  • JoannaBlackwelder
:-) Does that make sense?
anonymous
  • anonymous
yep
JoannaBlackwelder
  • JoannaBlackwelder
Cool, so what is the answer?
anonymous
  • anonymous
a
JoannaBlackwelder
  • JoannaBlackwelder
Yep!
anonymous
  • anonymous
can u do another plz?
anonymous
  • anonymous
;)
JoannaBlackwelder
  • JoannaBlackwelder
Sure
anonymous
  • 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
  • JoannaBlackwelder
Ok, well, let's see what happens if we do the same thing as the last problem.
JoannaBlackwelder
  • JoannaBlackwelder
What do you get when you sub 6x+9 for y in the second equation?
anonymous
  • anonymous
6x+9=6x+2?
JoannaBlackwelder
  • JoannaBlackwelder
Sweet! Can you simplify that?
anonymous
  • anonymous
combine like terms?
JoannaBlackwelder
  • JoannaBlackwelder
Yep
anonymous
  • anonymous
12x+9=+2??
anonymous
  • anonymous
@JoannaBlackwelder
JoannaBlackwelder
  • JoannaBlackwelder
No, to move one 6x to the other side, we need to subtract it
JoannaBlackwelder
  • JoannaBlackwelder
|dw:1440004496684:dw|
anonymous
  • anonymous
ohhhh i get it
anonymous
  • anonymous
so theres only one solution?
JoannaBlackwelder
  • JoannaBlackwelder
Sweet! So, any thoughts of what that tells us?
JoannaBlackwelder
  • JoannaBlackwelder
Hm, no. When the two equations simplify to a false statement (9 does not equal 2),
JoannaBlackwelder
  • JoannaBlackwelder
That means no solution
anonymous
  • anonymous
ohh
JoannaBlackwelder
  • JoannaBlackwelder
We can graph them to show that too.
JoannaBlackwelder
  • JoannaBlackwelder
They have the same slope, but different y intercepts
JoannaBlackwelder
  • JoannaBlackwelder
So they are parallel lines, and will never cross.
JoannaBlackwelder
  • JoannaBlackwelder
The solution is the point where the two lines cross.
anonymous
  • anonymous
one more??
JoannaBlackwelder
  • JoannaBlackwelder
Sure :-)
anonymous
  • 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
  • JoannaBlackwelder
Ok, any thoughts?
anonymous
  • anonymous
no
JoannaBlackwelder
  • JoannaBlackwelder
The first equation is solved for y.
JoannaBlackwelder
  • JoannaBlackwelder
So, we take what y is in terms of x, and plug it into the other equation.
JoannaBlackwelder
  • JoannaBlackwelder
Can you try to do that?
anonymous
  • anonymous
im lost, ugh and my online teacher keeps reminding me about time crunch lol
JoannaBlackwelder
  • JoannaBlackwelder
|dw:1440004939079:dw| Aw, that's frustrating!
anonymous
  • anonymous
i see
JoannaBlackwelder
  • JoannaBlackwelder
It is like the other ones, just the second equation isn't solved for y.
anonymous
  • anonymous
ho do i slove
anonymous
  • anonymous
how
JoannaBlackwelder
  • JoannaBlackwelder
We aren't supposed to solve, just substitute.
anonymous
  • anonymous
ok
JoannaBlackwelder
  • JoannaBlackwelder
|dw:1440005055460:dw|
JoannaBlackwelder
  • JoannaBlackwelder
See how I subbed the 3x+4 in for y in the second equation?
anonymous
  • anonymous
yes
JoannaBlackwelder
  • JoannaBlackwelder
That is all we have to do :-)
JoannaBlackwelder
  • JoannaBlackwelder
Which answer does that look like?
anonymous
  • anonymous
b
JoannaBlackwelder
  • JoannaBlackwelder
Right
anonymous
  • anonymous
one more, last one i promise lol
JoannaBlackwelder
  • JoannaBlackwelder
Haha, ok
anonymous
  • anonymous
d + e = 15 −d + e = −5 Label the ordered pair as (d, e). (0, 0) (10, −5) (5, 10) (10, 5)
JoannaBlackwelder
  • JoannaBlackwelder
Ok, this one we actually do have to solve. Any thoughts on how to start?
anonymous
  • anonymous
not really
JoannaBlackwelder
  • JoannaBlackwelder
Well, what happens when we add the two equations together?
anonymous
  • anonymous
we sub?
JoannaBlackwelder
  • JoannaBlackwelder
We could, but we would have to solve for one of the variables first.
anonymous
  • anonymous
ok
JoannaBlackwelder
  • JoannaBlackwelder
I would suggest to use elimination on this one. It is the easier method. :-)
anonymous
  • anonymous
ok
JoannaBlackwelder
  • JoannaBlackwelder
|dw:1440005374033:dw| What happens when we add the two equations together?
anonymous
  • anonymous
im not sure
JoannaBlackwelder
  • JoannaBlackwelder
Just take a guess
anonymous
  • anonymous
elimintion
JoannaBlackwelder
  • JoannaBlackwelder
Ok, but what equation are we left with?
anonymous
  • anonymous
i honestly don't know
JoannaBlackwelder
  • JoannaBlackwelder
|dw:1440005536799:dw| See how I added the equations together?
anonymous
  • anonymous
yes
JoannaBlackwelder
  • JoannaBlackwelder
Can you combine like terms?
anonymous
  • anonymous
ill be back in one min, my teacher is calling me
JoannaBlackwelder
  • JoannaBlackwelder
Ok
anonymous
  • anonymous
I'm back @JoannaBlackwelder
JoannaBlackwelder
  • JoannaBlackwelder
Ok, can you combine like terms?
anonymous
  • anonymous
that one is kinda hard
JoannaBlackwelder
  • JoannaBlackwelder
It is a little different. d-d is what?
anonymous
  • anonymous
d
JoannaBlackwelder
  • JoannaBlackwelder
No, it is like 2-2.
anonymous
  • anonymous
0
JoannaBlackwelder
  • JoannaBlackwelder
Right. :-)
JoannaBlackwelder
  • JoannaBlackwelder
And e+e is what?
anonymous
  • anonymous
e
JoannaBlackwelder
  • 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
  • anonymous
2
JoannaBlackwelder
  • JoannaBlackwelder
Close, 2e
anonymous
  • anonymous
oh i see
JoannaBlackwelder
  • JoannaBlackwelder
:-) And what is 15-5?
anonymous
  • anonymous
10
JoannaBlackwelder
  • JoannaBlackwelder
|dw:1440006758146:dw| Great!
JoannaBlackwelder
  • JoannaBlackwelder
See how I simplified that?
anonymous
  • anonymous
yep
JoannaBlackwelder
  • JoannaBlackwelder
Sweet, so we need to finish getting e by itself.
JoannaBlackwelder
  • JoannaBlackwelder
It is currently multiplied by 2
JoannaBlackwelder
  • JoannaBlackwelder
So, we need to divide the left side by 2 to leave just e (or 1e)
anonymous
  • anonymous
|dw:1440006877761:dw|
JoannaBlackwelder
  • JoannaBlackwelder
Good effort! But we need to divide by 2 to get e by itself, not 10
anonymous
  • anonymous
ok
JoannaBlackwelder
  • JoannaBlackwelder
|dw:1440006917075:dw|
anonymous
  • anonymous
ok
anonymous
  • anonymous
so whats my second point
JoannaBlackwelder
  • JoannaBlackwelder
Well, now that we know that e is 5, which answers do we have to choose from?
anonymous
  • anonymous
c,d
anonymous
  • anonymous
?
JoannaBlackwelder
  • JoannaBlackwelder
Are you sure that both c and d have e being 5?
anonymous
  • anonymous
c?
JoannaBlackwelder
  • JoannaBlackwelder
No, c, has e as 10.
anonymous
  • anonymous
d
JoannaBlackwelder
  • 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
  • anonymous
thank u
JoannaBlackwelder
  • JoannaBlackwelder
You're welcome

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