Answer:
x=3y-2
y=-3x-2
3y-x=-2
Step-by-step explanation:
we know that
To create a consistent and independent system, the slope of the other equation must be different at the slope of the given equation.
A consistent and independent system has only one solution
we have
y=3x-2
The slope of the given equation is m=3
so
Verify the slope of each case
case 1) we have
x=3y-2
isolate the variable y
3y=x+2 ------> y=(1/3)x+(2/3)
The slope is m=1/3
therefore
This equation can pair with the given equation to create a consistent and independent system, because their slopes are different
case 2) we have
y=-3x-2
The slope is m=-3
therefore
This equation can pair with the given equation to create a consistent and independent system, because their slopes are different
case 3) we have
y=3x+2
The slope is m=3
Parallel lines with different y-intercepts (The system has no solution)
therefore
This equation cannot pair with the given equation to create a consistent and independent system, because their slopes are the same
case 4) we have
6x-2y=4
isolate the variable y
2y=6x-4
y=3x-2
The slope is m=3
Is the same given equation (is a consistent and dependent system, has infinitely solutions)
therefore
This equation cannot pair with the given equation to create a consistent and independent system, because their slopes are the same
case 5) we have
3y-x=-2
isolate the variable y
3y=x-2
y=(1/3)x-(2/3)
The slope is m=1/3
therefore
This equation can pair with the given equation to create a consistent and independent system, because their slopes are different
