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Answer:
- graphing both equations is difficult
- (x, y) = (-35, -35 2/3)
- scaling is difficult
- "elimination" works well
Step-by-step explanation:
1. The equation x-y = 2/3 has no integer solutions, so is difficult to graph accurately.
The equation 4x -3y = -33 transforms to y = 4/3x +11, which is easy enough to graph, but has a slope so similar to the first equation that the graph is difficult to scale in a useful way. (The point of intersection is off the grid for the usual scaling we might choose.)
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2. The point of intersection is (x, y) = (-35, -35 2/3).
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3. As mentioned in part 1, the challenge is finding a useful scale and plotting points and lines accurately. (A graphing calculator helps immensely.)
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4. There are many ways to solve a system of linear equations. Here, "elimination" works well.
Rewrite the first equation to 3x -3y = 2. Subtract that from the second equation:
(4x -3y) -(3x -3y) = (-33) -(2)
x = -35
y = -35 -2/3 = -35 2/3 . . . . . from the first equation
The exact solution is (x, y) = (-35, -35 2/3).
