Question

For each system of linear equations shown below, classify the system as "consistent dependent," "consistent independent," or "inconsistent." Then, choose the best description of its solution. If the system has exactly one solution, give its solution. (THIS IS ONE QUESTION.)

Answer 1

System A:

$\begin{gathered} I)\text{ }y=-\frac{3}{2}x-4 \\ II)\text{ }3x+2y=-8 \end{gathered}$

Multiplying equation I by 2 we got:

I) 2y = -3x - 8

II) 3x + 2y = -8

Adding 3x on both sides of equation we got:

I) 3x + 2y = -8

II) 3x + 2y = -8

Since both equations are equivalent, this system must have infinitely many solutions. Therefore, it is a consistent dependent system.

System B:

I) y = -3x + 1

II) y = -3x

If we subtract equation II from equation I we reach the absurd statement "0 = 1". Theirefore, this is an inconsistent system.

System C:

$\begin{gathered} I)\text{ }y=-\frac{1}{2}x+\frac{5}{2} \\ II)\text{ }y=-2x+7 \end{gathered}$

Multiplying equation I by 2 we got:

I) 4y = -2x + 10

II) y = -2x + 7

Subtracting equation II from equation I we got:

3y = 3

y = 1

Then we have:

1 = -2x + 7

2x = 6

x = 3

Since this system has only one solution, it is a consistent independent system, with solution (3,1).