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The lines y=5x+3$, $y=-2x-25$ and $y=3x+k$ intersect at the same point. What is the value of $k$?

 May 23, 2019
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The lines y=5x+3$, $y=-2x-25$ and $y=3x+k$ intersect at the same point. What is the value of $k$?

 

y = 5x + 3         y  = -2x - 25          y = 3x + k

 

Set the first two equations equal for y.....solve for x

 

5x + 3  =  - 2x - 25

7x  =  - 28

x = -4

 

So  y =  5(-4) + 3  =  -17

 

So......the intersection point is   (-4, -17)

 

So

 

y = 3x + k       implies that

 

-17  = 3(-4) + k

-17= -12 + k

k = -5

 

Here's a graph : https://www.desmos.com/calculator/vgpkw03igb

 

cool cool cool

 May 23, 2019

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