Question

Solve the system 2x + 2y = -6 and 3x - 2y = 11 by using graph paper or graphing technology. What is the solution to the system?

(-1, -7)
(1, -4)
(2, -1)
(3, -2)
i got d

Answer 1

@jim_thompson5910

Answer 2

plot each equation on the xy axis system

I'd use something like desmos

https://www.desmos.com/calculator

Answer 3

the point where the two lines cross is the solution

Answer 4

i got 1,-4

Answer 5

correct

Answer 6

don't forget the parenthesis though

Answer 7

to graph a line you need a minimum of 2 points
the easiest to use what is x when y = 0 and what is y then x = 0
to find the solution as stated above find where the lines cross

Answer 8

At the end of May, Janet told Sam that she has read 10 books this year and reads 2 books each month. Sam wants to catch up to Janet. He tracks his book reading with a table on his door. Using his table below, what month will Sam have read the same amount of books as Janet?


Month Books
June 3
July 6
August 9
-November
-December
-January
-March
i got november?

Answer 9

This is throwing me off

`Janet told Sam that she has read 10 books this year and reads 2 books each month`

if she read 2 books each month, then she actually has read 2*12 = 24 books total for the year. How can they say she only read 10 books in a year?

Answer 10

I had a different approach.. that's why I was hesitant to answer
it said at the end of May she told Same that she read 10 books this year and reads 2 books each month

so it's at the beginning of the year... from January to May .. since the whole year hasn't be completed yet

Answer 11

oh that could be a possibility

Answer 12

@jim_thompson5910 will 2x-14 = 3x work where x is the month

Answer 13

I'm thinking that since it's at the end of May and we now know that it's 10 book and reads 2 a month

January -2
Febuary 2 and so on until May

Answer 14

omg lack of sleep. It's probably starting at January and then at the end of May it was revealed that she read 10 books so far this year... She reads 2 a month
so she was reading 2 books for 5 months..
January, Feb, March, April May

Answer 15

and he's like ok I'm going to catch up.... let me just start at June but instead of 2 a month, it's 3 a month

Answer 16

so he's like first month 3 books.. makes sense
first month x 3 books
1 x 3 = 3

Answer 17

second month x 3 books
2 x 3

third month x 3 books
3 x 3

and then I'm assuming that he takes a break and restarts in November
now fourth month x 3

Answer 18

So Sam's Chart was
Month Books
June 3
July 6
August 9
then we have November,
so he didn't read for September and October

that could be
Sept 0
Oct 0
November (resumes reading)
or something like that
and I see the multiples of 3 being used too before his break

Answer 19

-14 + 12 =-2 agree November

Answer 20

@triciaal you're on the right path

it should be 2x + 10 = 3x though

x = number of months since May
eg:
x = 0 represents may
x = 1 represents june
x = 2 represents july
etc

Answer 21

I also got November, but in a different style .

Answer 22

I don't like these problems too much.. worse than Mathematical Induction

Answer 23

@jim_thompson5910 thanks yes that works 2

Answer 24

The answer isn't Nov

Answer 25

triciaal also got November.. so why is it not November?

Answer 26

oh wait the equation isn't 2x + 10 = 3x

solve for x to get

2x + 10 = 3x
2x + 10-2x = 3x-2x
10 = x
x = 10

may is the 5th month
10 months from there is 5+10 = 15
the 15th month is really the 3rd month since 15-12 = 3

Answer 27

the table confirms it

Answer 28

so it would be March?

Answer 29

yes

Answer 30

the table confirmed

Answer 31

@UsukiDoll I had it wrong because I did 12 months not from May
5- 2 = 3 the 3rd month March

Answer 32

@triciaal I figured out my mistake . Apparently Sam's Chart blended into the Multiple choices so I assumed that Sam took breaks when in fact he didn't so he did started in June by reading 3 books a month until Sam can catch up with her.
So Sam was the multiple of 3 and she was the multiple of 2. With enough reading, both of them will catch up with each other in March for reading 30 books.

Answer 33

Janet was a multiple of 2 and started reading in January.. so by March she will have 30
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 (1 year and 3 months_
Sam was a multiple of 3 and started in June
0 0 0 0 0 3 6 9 12 15 18 21 24 27 30 (1 year and 3 months) Although he had a late start, adding one more book in his reading list proves to be successful later on.