From the second:
2x-y=4
x=(4+y)/2 and applying this to first:
4+y+3y=12
4y+4=12
4y=8
y=2 and since x=(4+y)/2, x=3 so
x+y=2+3=5
Compute successive differences of the terms.
If they are all the same, the sequence is arithmetic and the common difference is the difference you have found.
If successive pairs of differences have the same ratio, the sequence is geometric and the common ratio is the ratio you have determined.
Example of arithmetic sequence:
1, 3, 5, 7
Successive differences are 3-1 = 2, 5-3 = 2, 7-5 = 2. All the differences are 2, which is the common difference of the sequence.
Example of geometric sequence:
1, -3, 9, -27
Successive differences are -3-1 = -4, 9-(-3) = 12, -27-9 = -36. These are not the same, so the sequence is not arithmetic. Ratios of successive pairs of differences are 12/-4 = -3, -36/12 = -3. These are the same, so the sequence is geometric with common ratio -3.
I believe the correct answer from the choices listed above is option A. The <span>system can be changed so that the two equations have equal x-coefficients by multiplying </span><span>both sides of the top equation by 2 resulting to 6x + 4y = 24. Hope this answers the question.</span>
{ 3-y=2x
{ x+1/2y=3/2
{ -y=2x-3
{ 1/2y=3/2-x
{ y=-2x+3
{ y=3-2x
-2x+3=3-2x
(x,y) = (x,-2x+3)
