We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+2
536
1
avatar+19 

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

 

(a) \(\begin{align*} x+y&=-1,\\ 3x &= 4-3y. \end{align*}\)

 

(b)\(\begin{align*} 3x - 4y + 2&=0,\\ 10 - 10y& = 10y - 15x. \end{align*}\)

 

Thanks in advance!

 Jul 10, 2018
 #1
avatar+104686 
+1

a)

 

x + y  = -1

3x  = 4  - 3y

 

Rearrange the first equation as    y  = -1  - x

Sub this into  the second equation for  y

 

3x  = 4  - 3(-1 - x)   simplify

3x = 4 + 3 + 3x

3x  = 7 + 3x       dubtract   3x from both sides

0  = 7      this is absurd....so....this system has no solution

 

b)

 

3x - 4y  + 2   = 0  ⇒     3x  -  4y  = -2       (1)

10 - 10y  = 10y - 15x

 

Divide the second equation through by   5 and we have

2 - 2y  = 2y   - 3x       rearrange as

3x - 4y  = -2       (2)

 

Notice that equations 1  and 2 are exactly the same.....so....when this happens....we have  infinite solutions for both  x and  y

 

 

cool cool cool

 Jul 10, 2018

16 Online Users