I need help with points.... Please Help?

Question

Graph each system of equations and state its solution. Then state whether the system is consistent and independent, consistent and dependent, or inconsistent.

x + y = 6
x - y = -2


x + 1 = y
2x - 2y = 8


2x + 4 = 8
x + 2y = 4


x + y = 1
3x + 5y = 7

Answer 1

I'll do the 1st, not that you can draw a graph with a text only editor:

You let x and y take turns being zero and solve for the other variable. For x+y = 6, when x=0, y=6, so (0,6) is a point on the graph. When y=0, x=6, so (6,0) is a point on the graph. Draw a line through them. For x-y = -2, when x=0, y=2, so (0,2) is on the graph. When y=0, x= -2, so (-2,0) is on the graph. Draw a line through them. The lines intersect at (2,4), which is the solution of the system.

Since the lines intersect at 1 point, the system is consistent and independent. If the 2 lines had been parallel, it would be inconsistent. If the 2nd line had been right on top of the 1st, it would be consistent but dependent.

Answer 2

1)x+y=6
x-y=-2
2x=4
x=2

2+y=6
y=4
(2,4)

2)x+1=y
2x-2y=8
x-y=1
2x-2y=8
-2x+2y=-2
2x-2y=8
No solution

3)2x+4y=8
x+2y=4
2x+4y=8
-2x-4y=-8
No Solution

4)x+y=1
3x+5y=7
-5x-5y=-5
3x+5y=7
-2x=2
x=-1
-1+y=1
y=2
(-1,2)

In problems 1 and 4, they are consistent and independent. In problem 2, it is inconsistent. In problem 3, it is consistent and dependent.

I hope this helps!

Answer 3

in 1st equation x = 2 y = 4 They are consistent and dependent.

in 2nd equation they are inconsistent