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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
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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

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