Graphically Speaking
Graphically Speaking
 |
 Cricut Graphically Speaking Cartridge Brand New $4.24 (2 Bids) Time Remaining: 5h 46m |
 Cricut Graphically Speaking Cartridge Brand New $26.99 Time Remaining: 29d 22h 24m Buy It Now for only: $26.99 |
 Cricut Graphically Speaking Cartridge Brand New $0.99 Time Remaining: 6h 46m |
 Cricut Graphically Speaking Cartridge $25.00 Time Remaining: 4d 22h 13m Buy It Now for only: $25.00 |
 Cricut Graphically Speaking Cartridge Brand New $0.99 Time Remaining: 7h 46m |
 CRICUT Cartridge GRAPHICALLY SPEAKING Now Shipping NEW $42.95 Time Remaining: 3d 1h 26m Buy It Now for only: $42.95 |
 Cricut Graphically Speaking Cartridge Brand New $0.99 Time Remaining: 1d 5h 47m |
 CRICUT Graphically Speaking scrapbooking Cartridge $36.95 Time Remaining: 29d 23h 32m Buy It Now for only: $36.95 |
 Cricut Graphically Speaking Cartridge Brand New $0.99 Time Remaining: 1d 6h 46m |
 Cricut Graphically speaking expression create cartridge 29 0975 $36.94 Time Remaining: 4d 8h 53m Buy It Now for only: $36.94 |
 CRICUT CARTRIDGE GRAPHICALLY SPEAKING $2.99 (1 Bid) Time Remaining: 1d 7h 10m |
 New Cricut Cartridge GRAPHICALLY SPEAKING $34.99 Time Remaining: 3d 3h 3m Buy It Now for only: $34.99 |
 Cricut Graphically Speaking Cartridge Brand New $0.99 Time Remaining: 1d 7h 46m |
 CRICUT Graphically Speaking CARTRIDGE travel vacation signs icons ON SALE $27.99 Time Remaining: 6d 2h 57m Buy It Now for only: $27.99 |
 Graphically Speaking Cricut Cartridge Brand New $21.99 Time Remaining: 1d 9h 6m |
 GRAPHICALLY SPEAKING Cricut cartridge New in package $38.95 Time Remaining: 20d 34m Buy It Now for only: $38.95 |
 Cricut Graphically Speaking Cartridge Brand New $0.99 Time Remaining: 2d 5h 46m |
 GRAPHICALLY SPEAKING CRICUT Die Cutting Cartridge New $39.99 Time Remaining: 13d 4h 40m Buy It Now for only: $39.99 |
 Cricut Graphically Speaking Cartridge Brand New $0.99 Time Remaining: 2d 6h 46m |
 Cricut cartridge GRAPHICALLY SPEAKING words phrases numbers graphics moon travel $33.33 Time Remaining: 10d 12h 4m Buy It Now for only: $33.33 |
 Cricut Graphically Speaking Cartridge Brand New $0.99 Time Remaining: 2d 7h 46m |
 GRAPHICALLY SPEAKING Cricut Cartridge Brand NEW CC $32.99 Time Remaining: 9d 1h 59m Buy It Now for only: $32.99 |
 Cricut Cartridge GRAPHICALLY SPEAKING NEW GREAT PHRASES + ICONS FREE SHIPPING $28.95 Time Remaining: 4d 21h 51m Buy It Now for only: $31.95 |
 BRAND NEW Sealed Provo Craft Cricut Shapes Cartridges $49.99 Time Remaining: 25d 3h 51m Buy It Now for only: $49.99 |
 GRAPHICALLY SPEAKING CRICUT CARTRIDGE NIP $0.99 (1 Bid) Time Remaining: 2d 22h 28m |
Adding Methods in Special Cases?
Here is an example:
2x - 4y = 8
6x - 12y = 10
To solve this system, you would multiply the first equation by a -3 to make the x-values add out.
-3(2x - 4y) = -3(8) becomes -6x + 12y = -24
Put this new equation back with the second equation and then add the equations together.
-6x + 12y = -24
6x - 12y = 10
-----------------------
0 = -14
Notice how both the x-values and the y-values added out here. This leaves us with an equation that says 0 = -14. Is that true? Does zero equal negative fourteen? Of course not.
When this situation happens, we say there is "no solution." Graphically speaking these lines have the same slope and would be parallel.
--------
What I'm not understanding with this example is, why pick -3 to make the x-values add-out? Could anyone provide me with assistance?
Maybe, you may consider the following method:
y in terms of x—1st & 2nd equations:
2x - 4y = 8
x - 2y = 4
2y = x - 4
y = (x - 4)/2
6x - 12y = 10
3x - 6y = 5
6y = 3x - 5
y = (3x - 5)/6
Value of x:
6(x - 4) = 2(3x - 5)
3(x - 4) = 3x - 5
3x - 12 = 3x - 5
0 = 7 IS FALSE
Answer: This problem has no solution. Something is wrong with one or both equations.
Discussion
What do you think? Leave a comment. Alternatively, write a post on your own weblog; this blog accepts trackbacks [trackback url].