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1. For what ordered pair (a,b) are there infinite solutions (x,y) to the system
4x+ay=-8
2x+y=b

 

2. What is the y-intercept of the line x-2y=5?

 

3.Find the value of n that satifies \[frac{1}{n+1} + \frac{2}{n+1} + \frac{n}{n+1} = 3. \]

 Jun 13, 2019
 #1
avatar+103049 
+2

1.   4x + ay  = -8  (1)

      2x + y  = b           multiply through by 2  ⇒  4x + 2y = 2b     (2)

 

This will have infinite solutions  when (1) and (2) are the same

So    a  = 2

And  -8 = 2b  ⇒  b = -4

 

So  (a, b)  =  ( 2, - 4)

 

 

cool cool cool

 Jun 13, 2019
 #2
avatar+103049 
+2

2. What is the y-intercept of the line x-2y=5?

 

The y intercept occurs where x = 0......so....

 

(0) - 2y = 5

-2y = 5        divide both sides by  -2

y = -5/2   = the y intercept

 

cool cool cool

 Jun 13, 2019
 #3
avatar+103049 
+2

 

3.Find the value of n that satisfies   \(\frac{1}{n+1} + \frac{2}{n+1} + \frac{n}{n+1} = 3\)

 

[ 1 + 2 + n ]

__________   =    3                   multiply through by n + 1

     n + 1 

 

3 + n  =  3n + 3      subtract n, 3 from both sides

 

0 = 2n   

 

n = 0

 

cool cool cool

 Jun 13, 2019

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