An equation in the system is y = x + 1. what is the other equation in the system if the solution is only at (0, 1)?

You could construct another equation with a different slope and differen y intercept

y=mx+b
m=slope
b=yitertp

the slope in the given equation is 1
chang is

lets say the slope is 2
y=2x+b
(0,1)
(x,y)
1=2(0)+b
1=0+b
1=b
y=2x+1

it seems it can be y=mx+1 for all values of m except for m=1

some possible ones are
y=πx+1
y=-1x+1
y=-2x+1
y=3x+1
y=0.23432x+1
y=5x+1