Julian C. answered • 03/16/16

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Hi Sarah-

The first equation simplifies to y = -8. If you graph this in the plane, it will just be a horizontal line at y = -8. A horizontal line has slope 0, and here the y-intercept is -8. (If you want, you could think of this as y = 0x - 8.) If we're talking about the plane, "number of solutions" means the number of points on the line. Since a line has an infinite number of points, there are infinitely many solutions.

For the second equation, distribute to get 6 - 2x = 0, which solves to give x = 3. This is actually a vertical line at x = 3. (Think of all the points that have x value 3: they are all on a vertical line.) A vertical line has undefined slope, and this line has no y-intercept. Again, there are infinite solutions.

Julian

Sarah D.

03/17/16