How can we figure out how many cubes would be in the 10th step? Or the 100th?
1 answer:
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Ok so for part a we're going to use substitution, since both equations have y alone.
Step 1: Use substitution
y = x - 1 y = -x + 3
x - 1 = -x + 3
If you think about it, this makes sense. You're looking for the point where they intersect, and you know that the y coordinate for that point will be the same in both equations. Therefore, we can set the rest of the equations equal to each other. Now we just need to simplify.
Step 2: add x to each side
x - 1 + x = -x + 3 + x
The x's on the right cancel out so we get:
2x - 1 = 3
Step 4: Add 1 to each side
2x - 1 + 1 = 3 + 1
2x = 4
Step 5: Divide both sides by 2
2x/2 = 4/2
x = 2
Step 6: Plug this x value back into one of the original equations to find the y coordinate
y = x - 1
y = 2 - 1
y = 1
Therefore your answer to part a is (2,1)
I've graphed the solution and attached it. It shouldn't be too hard to replicate - just draw both lines and they should intersect at (2,1)
Hope that helps! If you need clarification or anything please feel free to ask :)
