+0  
 
+2
52
20
avatar+1720 

Need help asap, Could you maybe answer the first couple and I try the next ones? Then correct me if i'm wrong because i really want to understand this.

RainbowPanda  Aug 28, 2018
 #1
avatar+2983 
+3

(1) We have 3x+y=-2, 2x-3y=-5. We want to find a value of x that equals y. So, bringing 3x to the other side in the first equation, we get: y=-2-3x. The second equation: 2x-3y=-5, -3y=-5+2x, y=-5+2x/-3.

So, -2-3x=-5+2x/-3, so x=-11/7. Plugging the value of x in, in order to solve for y, we get: 3(-11/7)+y=-2, y=19/7.

tertre  Aug 28, 2018
 #2
avatar+1720 
+2

Is that all you do?

RainbowPanda  Aug 28, 2018
 #3
avatar+88775 
+2

Yep. after some manipulation as Tertre has done...... each problem wil have a variable already defined  in one of the equations...just substitute the value for that variable into the other equation ....you will  then have a variable in one equation that is easy to solve

 

BTW...thanks Tertre  !!!!

 

 

cool cool cool

CPhill  Aug 28, 2018
edited by CPhill  Aug 28, 2018
edited by CPhill  Aug 28, 2018
 #4
avatar+1720 
+1

Okay >.< I guess I could um try 6? or 7? uh idk 

RainbowPanda  Aug 28, 2018
 #5
avatar+88775 
+3

Try 6......post your answer....even if it's incorrect....we can  still fix that  !!!

 

 

 

cool cool cool

CPhill  Aug 28, 2018
 #6
avatar+1720 
+1

Oh shoot I started on 7 but ill do 6 as well hold on might take a bit

RainbowPanda  Aug 28, 2018
 #7
avatar+2983 
+3

Welcome! It was fun solving! 

tertre  Aug 28, 2018
 #8
avatar+1720 
+2

Okay so first....Am I even starting this off right. My head really hurts rn >.< like literally.

x+4y=-6-->4y=-6x

8x-2y=-14-->-2y=-14+8x

RainbowPanda  Aug 28, 2018
 #9
avatar+2983 
+2

Yes, now plug the value of y in terms of x.

tertre  Aug 28, 2018
 #10
avatar+1720 
+1

Okay um -2y=-14+8x divide by -2 on both sides so y=-14+8x/-2

4y=-6x divide by 4 on both sides as well and you get y=-6x/4

-6x/4=-14+8x/-2

So far so good? or am i totally wrong?

RainbowPanda  Aug 28, 2018
 #11
avatar+88775 
+2

You're not wrong...but  the there is an easier way without resorting to  those nasty  fractions

 

6)

x + 4y  = --6

8x  - 2y = -14

 

Do you see that we have a  single  variable in the first equation ???...in this case, x

So   subtract  4y  from  both  sides  and we get   x   = -6  - 4y

 

Now..in the second equatiion....just substitute this  for x  and we have

 

8 [ -6 - 4y ] - 2y  = -14    simplify

-48 - 32y - 2y  =  -14

-48  - 34y  = -14     add 48 to both sides

-34y = 34   divide both sides by  -34

y = -1

 

The beauty here is that  we already have an expression for x...we just need to fill in the y value

 

x = -6 - 4(-1)   =    -6 + 4   =  -2

 

So  (x, y)  = (  -2, -1)

 

 

As a hint on number 7...note that  7x  + y  = 7  can be transformed into   y = 7 - 7x

Can you take it from here???...post your work if you get stuck...I'll see if I can "un-stick" you  !!...LOL!!!!

 

 

 

cool cool cool

CPhill  Aug 28, 2018
 #12
avatar+1720 
0

My brain is about to explode, I can't do this >.<

RainbowPanda  Aug 28, 2018
 #15
avatar+88775 
0

Yes you can...you're close  !!!

 

 

cool cool cool

CPhill  Aug 28, 2018
 #13
avatar+1720 
+1

Oh wait I can try 7! 7x+y=7 ( subtract 7x from both sides)

y=7-7x

4x+3(7-7x)=21

(21-21x)

4x+21-21x=21

25x+21=21

-21        -21

25x do I divide it by 25 to get 1?

x=1

 

y=7-7(1)

y=7-7

y=0

(x,y)-->(1,0)

RainbowPanda  Aug 28, 2018
 #14
avatar+88775 
+2

Good try  !!!...  you have the right idea..just a small error

 

Let's take it from  here....

 

4x+3(7-7x)=21

 

4x + 21 - 21x  =  21     subtract  21  from both sides

 

4x  - 21x   =0

 

-17x  = 0   ⇒    x  = 0

 

Sub this back into y  = 7 - 7x  →  y  = 7 - 7 (0)    = 7  - 0   = 7

 

(x,y)  =(0,7) ...check this solution in both equations to see that this is true....!!!!

 

 

cool cool cool

CPhill  Aug 28, 2018
 #17
avatar+1720 
0

I knew I wouldn't have gotten it correct -_-

I tried 8 but it's obviously completely wrong. *sigh*

x+7y=23

-7y    -7y

x=23-7y

8(23-7y)-3y=7

184-56y-3y=7

and here is where it all goes wrong...

184-53y=7

-184      -184

53y=-177

/53     /53

y=-3.34 or something like that >.<

and i'll wait to see if i'm even correct first

RainbowPanda  Aug 28, 2018
 #18
avatar+88775 
+2

184-56y-3y=7

and here is where it all goes wrong...

 

LOL!!!!!.....Just a math error....

 

184 - 59y  = 7    subtract 184 from both sids

-59y  = -177  divide both sides by  -59

y  = 3

 

Sub this back into   x=23-7y   to  find x...and you're finished  !!!

 

You made a really good try...!!!

 

 

cool cool cool

CPhill  Aug 28, 2018
 #19
avatar+1720 
0

x= 2

y=3

(2,3)

Thanks I have 2 more that are a bit different cuz they involve 3 each and also a,b, and c. Would you be able to help with that seperately?

RainbowPanda  Aug 28, 2018
 #16
avatar+88775 
+1

Try 5  and note that     3x + y  = -2  ⇒   y  = -2- 3x

 

 

 

cool cool cool

CPhill  Aug 28, 2018
 #20
avatar+88775 
+1

If you're  still onboard...let me show you how to  solve these with something  known as  Cramer's Rule

 

Here's  6...which we know the answer to

 

x + 4y   = -6

8x  - 2y  = -14   we have the equations lined up properly....

 

Now  write the left side just using the coefficients

 

1    4

 -2        [ multiply  (1 * -2) diagonally  = -2  .....  subtract the product of the other diagonal =  (  8 * 4) = 32 ]

 

So we have    -2 -(32)   = -34       (1)         [as long as this isn't  0, we're  Ok]

 

Sub  the  -6  and  -14  into the 1st column  of  (1) ...this will  be the  "x" column"

 

-6    4      

-14  -2   [ repeat the process we just did...  (-6 * -2)   - ( 4 * -14)  = ( 12  - (-56) )  =    68

 

Divide this result by  the result  from (1)  and we get     68 / -34   =  -2   = x

 

Now  sub   -6 and -14 into the second column of (1)...this will be the "y" column ... and repeat the process

1   -6

8    -14          (1 * -14)  - ( -6 * 8)   =   ( -14 )  - ( -48)   =  -14  +  48  = 34

 

Divide this result  by (1)  to  get y   =   34/ -34  =  -1

 

So  (x, y) =   ( -2, -1)   ....exactly what we had before  !!!

 

 

 

cool cool cool

CPhill  Aug 28, 2018

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