Question

Solve the following system of equations:

x - 2y = 14
x + 3y = 9

(1, 12)

(-1, -12)

(12, -1)

(12, 1)

Answer 1

@ganeshie8 @satellite73

Answer 2

@texaschic101 @mathstudent55

Answer 3

@Luigi0210

Answer 4

do you prefer substitution or elimination ?

Answer 5

honestly idk how to even do this im so lost
and my teachers on vacation and cant help me ? whats the awnser do you think

Answer 6

x - 2y = 14
x = 2y + 14
now sub 2y + 14 in for x in the other equation

x + 3y = 9
2y + 14 + 3y = 9 -- subtract 14 from both sides
2y + 3y = 9 - 14
5y = -5
y = -1
now sub -1 in for y in either equation to find x
x - 2y = 14
x - 2(-1) = 14
x + 2 = 14
x = 14 - 2
x = 12

solution is (12,-1)

Answer 7

any questions ?

Answer 8

no none at all thank you do you mind helping me with some more?

Answer 9

Would been a bit simpler to multiply it by a negative.. x would of canceled :P

Answer 10

Solve the following system of equations:

-2x + y = 1
-4x + y = -1

(3, 1)

(-1, 3)

(-1, -3)

(1, 3)

Answer 11

thanks for helping too @Luigi0210

Answer 12

I will HELP.....we can go through it together

yes..Luigi....you could also solve it that way

Answer 13

can you isolate x in your problem Country Cuban ?

Answer 14

okay good i need someone to guide me through the steps show me how to slove the awnser and give me the awnser can you do that?

Answer 15

oops...isolate y in either of the equations

Answer 16

can you do that ?

Answer 17

wouldnt you at a positive 2 to the negative 2? and i think i can im not sure..

Answer 18

ok...your trying to do elimination. We can do it that way, or we can use substitution. You need to decide which way you want to do this. Elimination or substitution

Answer 19

elimnation

Answer 20

I can show you either way, or I can show you both ways

Answer 21

elimination would be easier:) show me how u get the awnser with elimination

Answer 22

-2x + y = 1
-4x + y = -1

we want to eliminate a variable, it does not matter which one. It would be easier to eliminate y by multiplying one of the equations (it does not matter which one) by a negative 1.

can you do that ?

Answer 23

then i have about 4 more problems that i need help on too after this :) could you help with those also?

Answer 24

I can

Answer 25

multiply one of those equations by a negative 1

Answer 26

do you want me to just do it and you can use my work for an example ?

Answer 27

so -4 times -1 = 4?

Answer 28

yes....-4 * -1 = 4

Answer 29

okay then what?\

Answer 30

so what would the solution be to this problem?

Answer 31

multiply everything in the equation by -1.
so what is y * -1 ? and what is -1 * -1 ?

Answer 32

do you want me to do the problem and you can use it as an example ?

Answer 33

-1,2

Answer 34

sorry idk what it is

Answer 35

and sure you could do that too if youd like

Answer 36

yes

Answer 37

-2x + y = 1
-4x + y = -1 --->(-1)
------------------
-2x + y = 1
4x - y = 1 (result of multiplying by -1)
-----------------add
2x = 2
x = 1

now sub 1 in for x in either equation to find y
-2x + y = 1
-2(1) + y = 1
-2 + y = 1
y = 1 + 2
y = 3

solution is (1,3)

Answer 38

do you have any questions ? about anything that I did

Answer 39

solution to that one is (1,3)

Answer 40

omg thanks @texaschic101 :)

Answer 41

alright here comes the next one

Answer 42

do you understand what I did ?

Answer 43

duhhhhhh

Answer 44

I am ready for the next one

Answer 45

and yes i understand :)

Answer 46

Solve the system of equations.

x + 3y = -1
2x + 2y = 6

(-4, 1)

(2, -1)

(4, -1)

(5, -2)

Answer 47

x + 3y = -1 --->(-2)
2x + 2y = 6
------------
-2x - 6y = 2 (result of multiplying by -2)
2x + 2y = 6
-----------add
-4y = 8
y = -2
now sub -2 in for y in either equation to find x
x + 3y = -1
x + 3(-2) = -1
x - 6 = -1
x = 6 - 1
x = 5

solution is : (5,-2)

Answer 48

wow that was alot better! are you ready for another?

Answer 49

what you got Texas boy ...lol

Answer 50

lol i got somethin for ya texas girl

Answer 51

and do you know how to change your name on openstudy to where u dont have to make a new account
?

Answer 52

no I do not......I have 2 accounts, each with different names, just in case I need it

Answer 53

oh okay could u ask some people cause i wanna change my name on here but dont know how and i dont wanna lose my fans

Answer 54

I can ask around

Answer 55

or just post that question in openstudy feedback section

Answer 56

let me do that haha

Answer 57

you got any more math questions ?

Answer 58

Solve the system of equations by substitution. What is the solution for x?

2x + y = 1
4x + 2y = -1

x = 0

x = 2

There is no x value as there is no solution.

x can be any value as there is an infinite number of solutions.

Answer 59

2x + y = 1
2x = -y + 1
x = -1/2y + 1/2

now sub -1/2y + 1/2 in for x in the other equation
4x + 2y = -1
4(-1/2y + 1/2) + 2y = -1 -- distribute through the parenthesis
-2y + 2 + 2y = -1 -- subtract 2 from both sides
0 = -3 (incorrect)
NO SOLUTION

Answer 60

thanks girl:) ready for another?

Answer 61

yep

Answer 62

alrighty :)

Answer 63

Determine which system below will produce infinitely many solutions.

-4x + 6y = 20
4x - 3y = -2

-2x + 4y = 18
4x - 8y = -36

3x - 2y = 5
-6x - 4y = -10

5x - 3y = 12
15x - 9y = 24

Answer 64

-2x + 4y = 18

4x - 8y = -36 -- divide by 2
2x - 4y = -18

so now we have :
-2x + 4y = 18
2x - 4y = -18
---------------add
0 = 0 (correct)

when the answer comes out equal, then there is infinite solutions
solution is option 2

Answer 65

thats my awnser ? "-2x + 4y = 18
4x - 8y = -36"

Answer 66

yes...answer is option 2

Answer 67

thanks 1 more/

Answer 68

Visitors to a carnival can buy an unlimited-ride pass for $50 or an entrance-only pass for $20. In one day, 282 passes were sold for a total of $10,680. How many unlimited-ride passes were sold?

114

146

168

212

@texaschic101

Answer 69

@ganeshie8

Answer 70

u + e = 282 --- unlimited + entrance only = 27 passes sold
50u + 20e = 10,680 -- 50 per unlimited + 20 per entrance only = 10,680

now we can solve by substitution...
u + e = 282
e = 282 - u
now we sub 282 - u in for e in the other equation..
50u + 20e = 10,680
50u + 20(282 - u) = 10,680
50u + 5640 - 20u = 10,680
30u = 10,680 - 5640
30u = 5040
u = 5040/30
u = 168....so there was 168 unlimited passes sold