Question

Systems of equations with different slopes and different y-intercepts have one solution.

Always
Sometimes
Never

Answer 1

@umm @Ultrilliam @Vocaloid @Elsa213 @Falconmaster @Felicity96

Answer 2

@563blackghost omg hi! can u please help me :)

Answer 3

Hey!

If the y-intercepts are different and the slopes are different then they would have no chance of being parallel. This would mean that this happens `Always`.

Answer 4

awesome! next :)


Breann solved the system of equations below. What mistake did she make in her work?

2x + y = 5
x − 2y = 10

y = 5 − 2x
x − 2(5 − 2x) = 10
x − 10 + 4x = 10
5x − 10 = 10
5x = 20
x = 4

2(4) + y = 5
y = −3

She should have substituted 5 + 2x
She combined like terms incorrectly, it should have been 4x instead of 5x
She subtracted 10 from both sides instead of adding 10 to both sides
She made no mistake

Answer 5

@563blackghost

Answer 6

Her first 2 steps are correct. She isolated y and plugged the equation into the second equation. She applied the distributive property perfectly and correctly combined like terms. She added 10 to both sides and then divided by 5 to get `x=4` which is correct. She plugged in 4 for x and simplified to get `y=-3`. `She made no mistake`

Answer 7

awesome next!! :)

There are 30 homes in Neighborhood A. Each year, the number of homes increases by 20%. Just down the road, Neighborhood B has 45 homes. Each year, 3 new homes are built in Neighborhood B.

Part A: Write functions to represent the number of homes in Neighborhood A and Neighborhood B throughout the years. (4 points)

Part B: How many homes does Neighborhood A have after 5 years? How many does Neighborhood B have after the same number of years? (2 points)

Part C: After approximately how many years is the number of homes in Neighborhood A and Neighborhood B the same? Justify your answer mathematically. (4 points)

Answer 8

So we highlight terms to see what function they may make.

`There are 30 homes in Neighborhood A. Each year, the number of homes increases by 20%.`

So we know we start with 30 so this will act as our `y-intercept`. We also know it increases by `20%` (we cannot have percents so we turn to decimal) this will act as our rate or `m`. So we get the equation \(\large\bf{y=.2x+30}\)

Answer 9

`Neighborhood B has 45 homes. Each year, 3 new homes are built in Neighborhood B.`

We apply the same process. We start with 45 `thus being our y-intercept`. and we know we have a rate of 3 new homes so this is our rate or `m`. We have the equation \(\large\bf{y=3x+45}\)

Answer 10

So we have Part A. Now we can work on Part B. Do you know on how to do that one?

Answer 11

hmmmm no not really

Answer 12

Well the equation tells us to plug in `5 years` for `Neighborhood A` and the `SAME` for `Neighborhood B`. So we do that.

\(\large\bf{A: ~~~y=.2({\color{red}{5}})+30}\)
\(\large\bf{B:~~~y=3({\color{red}{5}})+45}\)

What are the total houses for A and B?

Answer 13

let me solve them... give me on second

Answer 14

For A: 31
For B: 60

Answer 15

Correct! So we have part B down :)

Answer 16

awesome!

Answer 17

Ok I am stuck on this one, give me a lil while longer.

Answer 18

I tried substitution but I got `-4,93333...` O.o

Answer 19

hehe ok np

Answer 20

Wait. `Neighborhood A` says `increases by 20%` I do believe this would mean its exponential so the equation would be \(\large\bf{y=30+(.2)^{x}}\). Meaning for Part B it would be 30 houses. Sorry about that cookie.

Answer 21

oh its ok ! :)

Answer 22

I plugged to see on what C could be and this is what I got...

https://www.desmos.com/calculator/lfe9y4jbk4

Answer 23

I am sorry I can't be much help on this part :(

Answer 24

its ok! thanks ;)

Answer 25

np :)