Answer:
[tex](a)\ x = 3y - 2[/tex]
[tex](b)\ y = -3x - 2[/tex]
[tex](e)\ 3y - x = -2[/tex]
Step-by-step explanation:
Given
[tex]y =3x -2[/tex]
Required
Equations that can create consistent and independent systems
For a pair of equation to have consistent and independent systems, the equations must have different slopes.
An equation of the form [tex]y = mx + c[/tex] has m has its slope.
In [tex]y =3x -2[/tex]
[tex]m = 3[/tex] --- slope
Considering the options
[tex](a)\ x = 3y - 2[/tex]
Make y the subject
[tex]x = 3y - 2[/tex]
[tex]3y = x+2[/tex]
Divide by 3
[tex]y = \frac{1}{3}x+\frac{2}{3}[/tex]
The slope is:
[tex]m_1 = \frac{1}{3}[/tex]
Hence, (a) can make a consistent and independent system with [tex]y =3x -2[/tex]
[tex](b)\ y = -3x - 2[/tex]
The slope is:
[tex]m= -3[/tex]
Hence, (b) can make a consistent and independent system with [tex]y =3x -2[/tex]
[tex](c)\ y = 3x + 2[/tex]
The slope is:
[tex]m=3[/tex]
Hence, (c) cannot make a consistent and independent system with [tex]y =3x -2[/tex]
[tex](d)\ 6x - 2y = 4[/tex]
Make y the subject
[tex]2y = 6x -4[/tex]
Divide by 2
[tex]y = 3x -2[/tex]
The slope is
[tex]m =3[/tex]
Hence, (d) cannot make a consistent and independent system with [tex]y =3x -2[/tex]
[tex](e)\ 3y - x = -2[/tex]
Make y the subject
[tex]3y = x -2[/tex]
Divide by 3
[tex]y = \frac{1}{3}x -\frac{2}{3}[/tex]
The slope is:
[tex]m = \frac{1}{3}[/tex]
Hence, (e) can make a consistent and independent system with [tex]y =3x -2[/tex]
