Question

Can someone help me please??????
What is the value of the x variable in the solution to the following system of equations?
7x - 2y = 21
4x + y = 57

21

-21

9

-9

Answer 1

First get rid of y, so multiply the bottom by 2 and the two equations

Answer 2

is it C?

Answer 3

Did you work it out or are you guessing?

Answer 4

I worked it out but I don't think its right

Answer 5

Well don't doubt yourself kiddo, that's right :)

Answer 6

thank you :)

Answer 7

Anytime

Answer 8

can you help me with one more?

Answer 9

Sure

Answer 10

Rick works two jobs to pay for college. He tutors for $20 per hour and also works as a bag boy for $7 per hour. Due to his class and study schedule, Rick is only able to work up to 25 hours per week, but must earn at least $200 per week. If t represents the number of hours Rick tutors and b represents the number of hours he works as a bag boy, which system of inequalities represents this scenario?

t + b less than or greater to 25
20t + 7b greater than or equal to 200

t + b greater than or equal to 25
20t + 7b = 200

t + b less than or greater to 25
20t + 7b less than or greater to 200

None of the systems shown represent this scenario.

Answer 11

@whpalmer4
I think it might none but I'll get someone to help

Answer 12

tutoring and bagging time is up to 25 hours per week -> t+b <= 25

the first answer choice, is "less than or greater to" a typo?

Answer 13

same with the 3rd answer choice

well, \(t + b \le 25\) is one inequality

"he must earn at least $200/week" -> \(20t + 7b \ge 200\)

Answer 14

less than or equal to

Answer 15

the two inequalities are

\[t+b \le 25\]\[20t+7b\ge200\]

you decide if that appears on your answer list :-)

Answer 16

the third choice is < with line underneath

Answer 17

Thanks @whpalmer4 :)

Answer 18

you're welcome!

Answer 19

its A and thank you :)

Answer 20

@Luigi0210 hey, thanks for pushing me to 96 :-)

Answer 21

No Problem :D

Answer 22

celebration time, @jaderbrown, do you have another problem? :-)

Answer 23

yes :)
What is the value of the y variable in the solution to the following system of equations?
13x - 6y = 20
7x + 4y = 18

2

1

-2

-1

Answer 24

Okay, do you know how to solve by elimination?

Answer 25

yeah but I always get it wrong or stuck :(

Answer 26

let's see if we can change that :-)

Answer 27

@jaderbrown I told you not to doubt yourself >.<

Answer 28

so, which variable shall we eliminate? if we eliminate y, that looks a little easier, but then we need to solve for both x and y. if we eliminate x, then we don't have to solve for a second variable, but the arithmetic is a little uglier. your choice, we can do it both ways, too!

Answer 29

i know luigi lol, whpalmer can we do it both ways so I can understand it more?

Answer 30

sure. I'll do the ugly one first, then you can do the other one — anyone who saw both of our pictures would agree this is the right division ;-)

\[13x - 6y = 20\]\[ 7x + 4y = 18 \]I'm going to eliminate \(x\) by multiplying the first row by 7 and the second row by -13.

Answer 31

as they say at the magic show, watch my hands carefully :-)

Answer 32

\[7*13x - 7*6y = 7*20\]\[-13*7x-13*4y = -13*18\]a bit of arithmetic and then we have
\[~~~91x -42y = ~~~140\]\[-91x -52y = -234\]-------------------- add down the columns to get
\[(91-91)x +(-42-52)y = 140-234\]\[-94y = -94\]\[y = 1\]

Now we use the value of \(y\) in one of the original equations to find the value of \(x\):

\[13x-6(1) = 20\]\[13x-6=20\]\[13x=26\]\[x=2\]

Check with the other equation:
\[7(2)+4(1) = 18\]\[14+4 = 18\checkmark\]
[I'm not rechecking with the first equation because I used it to find \(x\) from \(y\)]

Answer 33

The key was just multiplying the first equation by the coefficient of the variable I wanted to eliminate in the second equation, and vice versa. I also multiplied (at the same time) by -1 so that they would be opposite in sign.

Answer 34

For some equations, you already have the coefficients with opposite signs, and then you don't need to do that step.

Answer 35

Okay, now it's your turn. The old surgeon's motto: "see one, do one, teach one" :-)

Answer 36

didn't you just solve for x and y?
so what do I do ?

Answer 37

you're going to do the same thing, except eliminate y instead of x.

Answer 38

you'll get the same answer, of course, breaking the curse that has dogged you :-)

Answer 39

okay hold on :)

Answer 40

i got stuck at x=6y+20 divided by 13

Answer 41

I don't think im doing it right at all. I looked at how you did it and Im not even close to what you did :(

Answer 42

im suppose to eliminate 13x so i divide it on each side and i divide it from 6y+20
so now what?

Answer 43

let's start at the beginning.

\[13x−6y=20\]\[7x+4y=18\]
You're planning to eliminate \(y\), and you've already got opposite signs there, right?

Answer 44

yeah

Answer 45

okay, so now we need to do something to those two equations that will get us a y coefficient in the first equation that is -<some number> and the y coefficient in the second equation is +<that same number>

Answer 46

what if you had the following fraction problem to do:

\[\frac{1}{6} + \frac{1}{4}\]
what would you use for a common denominator?

Answer 47

you'd probably use either 12 or 24, right?

Answer 48

use 12

Answer 49

okay. what do you need to multiply the first equation by to get the y coefficient to be -12?
then, what do you need to multiply the second equation by to get its y coefficient to be +12?

Answer 50

im confused, what are we doing to suppose to be getting 12 or -12?

Answer 51

we want the y coefficients to cancel out when we add the two equations together - elimination is the name of the game

Answer 52

okay so you add 6 to 20 so its 26
divide 13 from 26
x=2

Answer 53

did i do it right?

Answer 54

\[13x−6y=20\]\[7x+4y=18\]
what did you multiply with the first equation?
what did you multiply with the second equation?
(I just want to go through the steps to make sure you've got it all)

Answer 55

\[26x - 12y = 40 \text{ (assuming you multiplied by 2)}\]\[21x+12y=54\text{ (assuming you multiplied by 3)}\]------------------\[47x + 0y = 94\]

Answer 56

the solution to that is clearly \(x =2\)
I'm just not quite sure about your "okay so you add 6 to 20 so its 26/ divide 13 from 26"
maybe you could show a little more detail?

Answer 57

well I just did the first equation but do I have to do the second one?

Answer 58

that's entirely up to you. you do already know the answer, but a little practice is always good.

Answer 59

i think I got it :)

Answer 60

okay, well, I'm off to another problem! good night...