Answer:
y = x -4
y = 2x - 7
(answers may differ depending on slope chosen, see below)
Explanation:
use the point-slope form for a linear equation, which is
(y-y₁) = m(x-x₁)
recall m = slope and (x₁,y₁) are simply any point on the line
in our case, since both equations have (3,-1) as solutions, that means both lines intersect at (3,-1) which also means that for both equations, x₁=3 and y₁=-1
hence the equation becomes
(y-(-1) ) = m(x-3)
(y+1) = m(x-3)
y+1 = m(x-3)
in order to express the above equation as 2 different equations with the same (x₁,y₁), all we need to do is to choose 2 random values for m
we'll pick m = 1 and m = 2 which gives us our 2 equations
y+1 = x-3 (rearranging)
y = x -4
and
y+1 = 2(x-3) (rearrange)
y = 2x - 7