At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
not really I'm so confused
Ok, they are using the method of substitution.
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.
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.
But have you followed what I have said so far?
So, if you plug in x+1 for y in the second equation, what do you get?
Hm, no, if we are subbing x+1 in for y, then we don't have y anymore.|dw:1440004062537:dw|
:-) Does that make sense?
Cool, so what is the answer?
can u do another plz?
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
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?
Sweet! Can you simplify that?
combine like terms?
No, to move one 6x to the other side, we need to subtract it
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
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.
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)
Ok, any thoughts?
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!
It is like the other ones, just the second equation isn't solved for y.
ho do i slove
We aren't supposed to solve, just substitute.
See how I subbed the 3x+4 in for y in the second equation?
That is all we have to do :-)
Which answer does that look like?
one more, last one i promise lol
d + e = 15 −d + e = −5 Label the ordered pair as (d, e). (0, 0) (10, −5) (5, 10) (10, 5)
Ok, this one we actually do have to solve. Any thoughts on how to start?
Well, what happens when we add the two equations together?
We could, but we would have to solve for one of the variables first.
I would suggest to use elimination on this one. It is the easier method. :-)
|dw:1440005374033:dw| What happens when we add the two equations together?
im not sure
Just take a guess
Ok, but what equation are we left with?
i honestly don't know
|dw:1440005536799:dw| See how I added the equations together?
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.
And e+e is what?
No, we add the coefficients, and when there is no coefficient written it is understood to be 1. So this is 1e+1e
oh i see
:-) And what is 15-5?
See how I simplified that?
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)
Good effort! But we need to divide by 2 to get e by itself, not 10
so whats my second point
Well, now that we know that e is 5, which answers do we have to choose from?
Are you sure that both c and d have e being 5?
No, c, has e as 10.
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. :-)