We have the next system of equations
x + y = 6
3x - 4y = 4
First, we will isolate the x of the first equation
x=6-y
then we will substitute the equation above in the second equation
3(6-y)-4y=4
Then we simplify
18-3y-4y=4
we sum like terms
-7y=-18+4
-7y=-14
y=-14/-7
y=2
then for x
x=6-2
x=4
Because we obtain one solution we can say that the system is independent and consistent
If we want to solve by graphing we need to graph each equation by calculating some points
For the first equation
x+y=6
we isolate the y
y=-x+6
x=0
y=6
Point (0,6)
x=-3
y=-(-3)+6
y=9
Point (-3,9)
For the second equation
3x-4y=4
we isolate the y
y=3/4x-1
x=0
y=-1
Point (0-1)
x=-4
y=3/4(4)-1
y=-3-1=-4
Point (4,2)
Then we graph the lines by connecting the points we calculate
The line in blue is x+y=6
The line in green is 3x-4y=4
The point where the two lines intercept each other is the solution in this case (4,2) as we can verify previously
Because the lines intercept in only one point we can say that the system of equations is consistent and independent