+0  
 
+2
49
1
avatar

Solve each of the following systems of equations. Find all solutions.

a.



(b)

Your Response:

Guest Feb 8, 2018
Sort: 

1+0 Answers

 #1
avatar+82944 
+1

x + y  =  -1    subtract x from both sides ⇒  y    =  - 1 - x   (1)

3x  =  4 - 3y      (2)

 

Note that we can put (1)   into (2)...and we have that

 

 

3x  =    4  -  3 [ 1 - x ]     simplify

 

3x  =  4  - 3  + 3x     if we subtract  3x from both sides we have

 

0  =  4 -3

 

0  = 1    This is never true...so.....strangely.....we have no solutions  for x and y !!!

 

 

 

3x  - 4y  + 2  =  0

10 - 10 y   =  10y  - 15x

 

Divide the second equation through by 5  and we get

 

2 - 2y = 2y - 3x

 

Add 3x to both sides....subtract  2, 2y from both sides

 

3x - 4y   =  - 2    (1)

 

 

Subtract 2 from both sides of the first equation  and we have

 

3x - 4y   =  -2     (2)

 

Notice that the transformed equations are exactly the same......whenever this occurs, we have  infinite solutions for x and y  !!!!

 

One way to express this is to let x be "fixed"  and  solve any of the equations for y

 

So......

 

3x - 4y = -2 

 

3x + 2  = 4y

 

[ 3x + 2 ] / 4  = y

 

 

So....the solution set can be expressed as  {x , y }   =  { x , [3x + 2] / 4 }

 

 

 

 

 

cool cool cool

CPhill  Feb 8, 2018

8 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details