+0

+2
250
20
+2448

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.

Aug 28, 2018

#1
+4221
+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.

Aug 28, 2018
#2
+2448
+2

Is that all you do?

RainbowPanda  Aug 28, 2018
#3
+100516
+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  !!!!

CPhill  Aug 28, 2018
edited by CPhill  Aug 28, 2018
edited by CPhill  Aug 28, 2018
#4
+2448
+1

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

RainbowPanda  Aug 28, 2018
#5
+100516
+3

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

CPhill  Aug 28, 2018
#6
+2448
+1

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

RainbowPanda  Aug 28, 2018
#7
+4221
+3

Welcome! It was fun solving!

tertre  Aug 28, 2018
#8
+2448
+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
+4221
+2

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

tertre  Aug 28, 2018
#10
+2448
+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?

Aug 28, 2018
#11
+100516
+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!!!!

CPhill  Aug 28, 2018
#12
+2448
0

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

RainbowPanda  Aug 28, 2018
#15
+100516
0

Yes you can...you're close  !!!

CPhill  Aug 28, 2018
#13
+2448
+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)

Aug 28, 2018
#14
+100516
+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....!!!!

CPhill  Aug 28, 2018
#17
+2448
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
+100516
+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...!!!

CPhill  Aug 28, 2018
#19
+2448
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
+100516
+1

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

Aug 28, 2018
#20
+100516
+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  !!!

Aug 28, 2018