Which choice is the explicit formula for the following geometric sequence?0.5, -0.1, 0.02, -0.004, 0.0008, ...
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For 1 and 2, you plot both lines, and wherever they intersect is the solution to the system. Given the equation of a line, I think the easiest way to plot it is to find two points on the line, then draw a line through them. For example, if , then when
, you get
; when
, you get
. So plot the points (0, -1) and (1, 4), then strike a line through.
1. Notice that dividing both sides of by 2 returns
, same as the first equation. So the system of equations reduces to one equation, which can have an infinite number of solutions. (This is because for any choice of
or
, you can always find a corresponding value for the other variable.)
2. See attached image. is given by the purple line.
For 3-6, you have several options. The two simplest methods of solving them are by substitution or elimination.
3. Like with (1), notice that dividing both sides of the first equation by 2 gives , so there will be an infinite number of solutions.
4. (by substitution) Since , we can replace
in the second equation:
but this is false, so there are no solutions to this system.
5. (by substitution) Since , in the first equation we have
Then back in the second equation we find
So (-4, -3) is the only solution here.
6. (by substitution) Notice that the left hand sides of both equations are the same, so we end up with 7 = 12, but this is false, so no solution exists.
So my understanding from this you have to make it y = mx + b so m stands for the slope there’s different ways to find it as shown in the first picture. I’ll try to make another comment since this only lets me take one picture at a time.
