I tried solving these but I gave up lol I could only get to the parts where you add the x values and add the y values

For example, for number 1, 7x+-14x=-7x and 2y-3y=-1y (you would only add if there is a + right?)

And then add -10+29= 19 so I got to -7x+-1y=19 but i don't even know if I did that right. I got stuck there.

RainbowPanda
Aug 28, 2018

#1**+4 **

The keys to solving these

(1) line up all variables on one side of the equation and constants on the other

(2) pick a variable to eliminate....either will do....this is the REAL key

(3) not a necessity...but I always like to get rid of fractions, too, before I start

7x + 2y = -10

-14x - 3y = 29

I see that if I multiply the top equation by 2 and add it to the second equation, the "x" term will disappear..so

14x + 4 y = -20

-14x - 3y = 29 add these and we get

y = 9

To find x...we can use any equation...so...

7x + 2(9) = -10

7x + 18 = -10

7x = -28

x = -4

So.....(x, y) =(-4, 9)

Do you want to try a couple on your own, RainbowPanda ??

CPhill
Aug 28, 2018

#2**+2 **

@CPhill, 29 or -29? This was in step 2.

(2) Multiply the second equation by 2, so: -9x-14y=-29, 10x+7y=-2, -9x-14y=-29, 20x+14y=-4..

So, adding: y gets canceled, and 11x=-33, \(x=-3\), so y= -9(-3)-14y=-29, 27-14y=-29, 14y=27+29, 14y=56, \(y=4.\)

tertre
Aug 28, 2018

#4**-2 **

Nobody is going to help you. You should probably pay more attention in class. I guess that means you're kind of dumb. πΈπ°ππππ©.

Can you answer me this, what is 2+6578901+51784946% and -17264967+-837956881868078.

Guest Aug 28, 2018

#5**+2 **

4) -20 + 10 x = -10y

45 = 6x - 27 y

Rearrange each as

10x + 10y = 20

6x - 27 y = 45

I see that I can divide the top equation by 10 and the bottom by 3 to get :

x + y = 2

2x - 9y = 15

I see that I can eliminate 'x" by multiplying the top equation by -2

-2x - 2y = -4

2x - 9y = 15 add these

-11y = 11

y = -1

And using any equation to find x, we have

x + y = 2

x + (-1) = 2

x - 1 = 2

x =3

So (x,y) = (3 , -1)

Do these steps help ???

CPhill
Aug 28, 2018

#6**+3 **

(4) Hint: Try to rearrange the equation, the first and second: Take -10y to the other side, and see what you can do.

tertre
Aug 28, 2018

#10**+2 **

Thank you so much for your help, both of you. I have tried it and yet i'm still too dumb to solve these. >.<

RainbowPanda
Aug 28, 2018

#11**+3 **

You're not "dumb"....it's just hard to get the hang of this...

I'll do 2) and 3).....maybe that will help some

2) - 9x - 14y = -29

10x + 7y = -2

Ok....do you see that we can eliminate y by multiplying the second equation by -2 ??...so we have

-9x - 14 y = -29

20x + 14y = -4 add these

11x = -33 divide by 11

x = -3

Using 10x + 7y = -2 to find y, we have

10(-3) + 7y = -2

-30 + 7y = -2 add 30 to both sides

7y = 28 divide by 7

y = 4

So...(x, y) = ( -3, 4)

CPhill
Aug 28, 2018

#12**+3 **

3) 0 = -36x + 14y + 8

0 = 18y - 9 - 27x

Rearrange these as

36x - 14y = 8

27x - 18 y = -9

Divide the first equation through by 2 and the second one through by 9

18x - 7y = 4

3x - 2y = -1

I see that we can get "-18x" by multiplying the second equation by -6 ...so we have

18x - 7y = 4

-18x + 12y = 6 add these

5y = 10 divide by 5

y = 2

Using 3x - 2y = -1 to find x, we have

3x - 2(2) = -1

3x - 4 = -1

3x = 3 divide by 3

x = 1

So (x,y) = ( 1, 2)

CPhill
Aug 28, 2018

#14**+3 **

It's just that some of the problems are different so it makes it harder to understand and to know you are doing the problems correctly because you can't go off of one problem if they are even the slightest bit different. Am I even making sense right now xD

Thank you for helping~

RainbowPanda
Aug 28, 2018

#16**+1 **

Problem is there is also other ways of solving these problems like solving the system of equations by substitution and of course elimination.

RainbowPanda
Aug 28, 2018

#13**+3 **

For (3). Just take the constant to the other side, you're left with x and y= constant.

Here, I'll show you!

0=-36x + 14y + 8

0 = 18y -9 -27x

Best thing to do first: 36x - 14y = 8 - 0, 36x - 14y = 8

And, for the second equation: 27x - 18y = 0+9, 27x - 18y = -9.

Now, divide the first equation by 2 and the second equation by 9, because the x will end up as a canceling factor.

So, 18x-7y=4, 3x-2y=-1, try to make both x's equal, subtract find x, then solve for y!

mathtoo
Aug 28, 2018