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