Open Middle®
Directions: Using the integers -9 to 9 at most one time each, place an integer in each box to create a system of equations with a solution in that’s as close to the origin as possible.
Hint
How can you tell which solution is closer to the origin?
Answer
The solution that is closest to the origin is y = (-9/-1)x + 1 and y = (-2/9)x + 0, which has a solution at (-9/83, 2/83).
Source: Robert Kaplinsky
Even closer to zero system is: y=9/8x+0 and y=-9/1x+-1 it hits the point (8/81, 1/9)
I stumbled upon this by accident:
y = (9/1)x+(-1) and y = (-4/4)x+0
The intersection is (1/10, -1/10)
How about
y = (-9/-1)x + 1 and y = (-2/9)x + 0 ?
That intersection is (-9/83, 2/83).
yea that is weird that they didn’t catch -9/83 and 2/83
Thank you Ryan! We have updated the answer.
y=9/-9+0
y=-1/1+1