help me with graphing?

Question

this is "system of equations"


and i need to graph


x+y=12
x-y= -6


I need to find (?,?),(?,?)


but im lost..

Answer 1

Convert both equations into standard from y=mx +b

X being the slope B is the y intercept.

y=-x+12..Has a -1 for a slope and 12 for the y intercept
y=x+6...Has a 1 for a slope and 6 for the Y intercept..

OK notice that the slopes are negative reciprocals of one another..Therefore these are perpendicular lines..

I did not understand what two points that you are looking for..But I am assuming you are looking for the intersection of these lines.

This will happen when -x + 12 = x +6
12 = 2X + 6
6 =2x
x=3

Plug this x value into both equations to find the y coordinate and VOILA that is your intersection..

(3,9) in case you are too stressed out to finish it =)

Answer 2

Solve both of these for y(x):
y = 12 - x = -x + 12
-y = -6 - x or y = x + 6
Two points determine a straight line; there is no power to the x so these are both straight lines.
Start with the first line:
y(0) = 12 so one point would be (0,12)
0 = -x + 12 or x = 12, so another point would be (12,0)
Now for the second line:
y(0) = 6 so the first point is (0,6)
0 = x+6 or x = -6 and the second point is (-6,0)
For both you have two points making it easy for you to plot and just draw the lines.
Try this on a few others and you will get it

Answer 3

Consider line x + y = 12:-
(0,12) and (12,0) are points on this line so line can be drawn.

Consider line x - y = - 6:-
(- 6,0) and (0,6) are points on this line so line can be drawn.

Point where lines intersects is solution to the equations:-
x + y = 12
x - y = - 6
2x = 6
x = 3 , y = 9 is solution to equations and thus when you draw the lines, they should intersect at (3 , 9)

Answer 4

x+y=12 ---> y= -x+12

x-y= -6 ---> -y= -x -6 ---> y= x+6

graph y intercept, then slope...
then i think where the two lines intercept is the answer?...

Answer 5

use the addtion method...

add the second equation to the first one..
y's cancel out... and you get... 2x=6
so, x=3

plug in this number to either equation...
and you get y=9

so the ordered pair is .... (3,9)