Question

math :(

Answer 1

Solve the following system by using graph paper or graphing technology.

–3x + y = 2
–9x + 3y = 6

What is the solution to the system?

No Solutions

Infinite Solutions

(3, 2)

(9, 2)

Answer 2

i think it is A

Answer 3

you dont need to graph
\[\qquad-3x+y=2\]
\[ -9x + 3y = 6\]\[\cancel3(-3x+y)=\cancel3(2)\]

these equations are the same,

the two lines are on top of each other

Answer 4

so it would be Infinite Solutions right?

Answer 5

the is a line of solutions

Answer 6

so what would the answer be?

Answer 7

i dont like any of those answers

Answer 8

but i guess a line has an infinite number of points

Answer 9

ok thanks

Answer 10

Use a system of equations to solve the following problem: Charles High School has a total of 94 boys and girls who play sports. If the number of boys is 22 more than twice the number of girls, how many boys play sports at this high school?

70

48

24

80

Answer 11

what do you know about the total number of boys and girls?

Answer 12

what is the total number of boys and girls?

Answer 13

i am not sure :(

Answer 14

read it

Answer 15

94

Answer 16

okay sweet so theres 94 boy and girls total

Answer 17

yes

Answer 18

what we want to do is is write an equation using this information

Answer 19

22+2x = 94

Answer 20

would you agree with me that if there are 94 boys and girls total thats basically the same as saying:

boys + girls = 94

Answer 21

yes!

Answer 22

yes

Answer 23

\[94=b+g\]\[ b -22= 2 \times g\]\[b=?\]

Answer 24

and the second equation is the one you posted

Answer 25

what we do is use both those equations to "solve the system"

Answer 26

isolate a variable in one equation and substitute that into the other equation

Answer 27

basically theres only one certain number of boys and one certain number of girls that satisifys these conditions:

boys + girls = 94

and!!

boys = 22 + 2 (girls)

Answer 28

lets let the boys be y
and the girls be x

Answer 29

ok

Answer 30

what would our equations be now?

Answer 31

y=22x

Answer 32

that is wrong

Answer 33

just change the girls to x

Answer 34

and the boys to y

Answer 35

x=22y

Answer 36

boys + girls = 94
boys = 22 + 2 (girls)

Answer 37

x+y=94
x=22+2

Answer 38

wait one little mistake in there...

Answer 39

:(

Answer 40

boys + girls = 94
boys = 22 + 2 (girls)

Answer 41

change all the boys to one letter and all the girls to another

Answer 42

look at the second equation

Answer 43

boys=y
girls=x
y+x=94
y=22+2

Answer 44

better?

Answer 45

I see a girls next to the very last 2...

Answer 46

boys = 22 + 2 (girls)

Answer 47

y=22+2(x)

Answer 48

yes!

Answer 49

so now we have two equations

Answer 50

we can now "solve the system"

Answer 51

y+x=94
y=22+2x

Answer 52

the bottom equation says that y equals "22 +2x"

Answer 53

so lets just go to the top equation and change y to "22 + 2x"