x+y=2 , x+y=0 , solve it

Question

i have 2 question ,  our teacher give us 2 parallel  problem  but i did not solve it please help me

 

1.  x+y=2 , x+y=0 , solve it ?

2.  x+y=3 , 2x-2y=6, solve it ?

Answer 1

1) x+y=2 and x+y=0 ate parallel lines that never touch.
Putting them into slope intercept form of y=mx+b where m is the slope of the line and b is the y-intercept gives us:
y=-x+2 and y=-x both lines have a slope of -1 and never touch.
There is no solution for the system... so it is the empty set {}

2)

 

x+y=3 equation 1
2x-2y=6 equation 2

multiply equation 1 by 2 to change y to 2y so that we can eliminate the y variable by adding the equations together

2x+2y=6 (equation 1)(2)
2x-2y=6
_________

4x+0y =12
4x=12
x=3

plugging 3 in place of x in either beginning equation gives:

3+y=3 equation 1
y=0

The solution set is the point (3,0)
Which means that is the only point common to both lines

Answer 2

Another way to look at it.

 

(x + y)  is  equal to both 0 and 2.  However, 0 and 2 do not equal each other.  This means that if you had numbers x and y that give you the sum of 0, those same numbers will NOT give you the sum of 2; and vice-versa.  Therefore, no value of x and y satisfy both equations.

Answer 3

The first set of equations when put slope/intercept form are y=2-x and y=-x and since the slopes of the two lines are the same (-1) they will not intersect so there is no solution.

The second set can be written as y=3-x and y=x-3 so 3-x=x-3 or 2x=6, x=3 and y=0 is the solution. This set of lines are perpendicular to each other since the product of their slopes equals -1.

 

Hope this helps

 

Jim