Solve each of the following systems by graphing
x - 2y = 8
3x - 2y = 12
2007-07-20 07:47:57 · 11 answers · asked by Dawn M 1 in Science & Mathematics ➔ Mathematics
x - 2y = 8
x = 8 + 2y
3x - 2y = 12
3x = 12 + 2y
x = (12 + 2y) / 3
8 + 2y = (12 + 2y) / 3
3(8 + 2y) = (12 + 2y)
24 + 6y = 12 + 2y
4y = - 12
y = - 3
x = 8 + 2(- 3)
x = 8 - 6
x = 2
Answer: x = 2, y = - 3
Proof:
2 - 2(- 3) = 8
2 + 6 = 8
3(2) - 2(- 3) = 12
6 + 6 = 12
2007-07-23 01:42:16 · answer #1 · answered by Jun Agruda 7 · 2⤊ 0⤋
pretty hard to graph in a text box, but:
x - 2y = 8 is equivalent to y= (1/2) x -4. that is a line that slopes up to the right with a slope of 1/2 and a y intercept of (-4)
3x - 2y = 12 is the same as y=(3/2)x-6 which is a line sloping up to the right with a slope of 3/2 and a y intercept of (-6)
to see actual graphs you can go to:
http://gcalc.net/
and type in
0.5x-4 for the first one and
1.5x-6 for the second one
once you have those, you just find the intersection to solve the system! The answer is (2,-3) but i solved it without graphing...
2007-07-20 07:51:52 · answer #2 · answered by yerffej9 2 · 1⤊ 0⤋
Consider the value of:
x co-ordinate to be -1 0 & +1
now substitute these values in the eqn: x - 2y = 8
x - 2y = 8
-1 - 2y = 8
-2y = 8 + 1
-2y = 9
y = -9/2
there for the first set of co-odinates for you to plot is (x, y) = (-1, -9/2) or (-1, 4.5)
just like this after substituting x = 0
you will get (x, y) = (0, -4)
and the 3rd time substitute x = +1
you will get (x, y) = (+1, -7/2) = (0, -3.5)
so you have the 3 points to plot on your graph paper.
PLEASE FOLLOW THE SAME METHOD FOR THE SECOND SUM TOO. You will find your co-ordinated.
All the best... umm may i ask a question? Did i just do your homework?
:) cheers
ritu
2007-07-20 08:01:01 · answer #3 · answered by ritukiran16 3 · 0⤊ 2⤋
x - 2y = 8
(0 , - 4) and (8 , 0 ) are two points on this line.
The line may thus be drawn.
3x - 2y = 12
(0 , - 6) and (4 , 0) are two points on this line.
The line may thus be drawn.
Point of intersection of lines gives solution to the given set of equations.
As a check, the point is (2 , - 3)
2007-07-20 20:23:58 · answer #4 · answered by Como 7 · 0⤊ 0⤋
x= 14 - 2y = 8
y= 3
14 - 6 = 8
3x - 2y = 16
x=6
y=3
18- 6 = 12
2007-07-20 07:58:05 · answer #5 · answered by Mii 1 · 0⤊ 2⤋
y = 3 and x = 14
2007-07-20 07:54:43 · answer #6 · answered by Anonymous · 0⤊ 2⤋
-x + 2y =- 8
3x - 2y = 12
2x=4
x=2
y=-3
(2,-3)
draw two lines by finding arbitrary two points for each line
2007-07-20 07:54:03 · answer #7 · answered by iyiogrenci 6 · 0⤊ 1⤋
Yes, those are math problems. X represents the horizontal axis on the graph and Y represents the vertical axis. You can easily graph these numbers by starting with whole numbers with X, such as 0, 2, etc. I would use even numbers because that looks easier to find. You don't need to figure out every last point because these look like straight lines... Algebra I?
2007-07-20 07:52:58 · answer #8 · answered by Cheshire Cat 6 · 0⤊ 2⤋
put each in the form of y = mx + b where m is the slope and b is the y-int...
1st: y = 1/2x - 4
2nd: y = (3/2)x - 6
Graph to find the intersection..
Otherwise, by paper:
1st: y = 1/2x - 4
Plugging in to 2nd: 3x - 2(1/2x - 4) = 12
3x - x + 8 = 12
2x = 4
x = 2
Plug back in to 1st:
y = 1/2*(2) - 4
y = -3
Ans: (2, -3)
2007-07-20 07:53:40 · answer #9 · answered by miggitymaggz 5 · 1⤊ 2⤋
Take the letters out and maybe I can answer it
2007-07-20 07:51:37 · answer #10 · answered by Anonymous · 0⤊ 2⤋