wegnerkolmp2741o

Answer:

a  inconsistent

b  consistent

c consistent

Step-by-step explanation:

3a.  Multiply the first equation by -4

-4(-3x+4y) = -4(3)

Distribute

12x -16y = -12

Add this to the second equation to eliminate x

12x -16y = -12

-12x +16y = 8

-----------------------

         0 = -4

This is not true, so there are no solutions.  This means the system is inconsistent.

3b.  Multiply the first equation by -2

-2(7x+3y) = 0*-2

-14x -6y = 0

Add this to the second equation to eliminate x

-14x -6y = 0

14x+6y = 0

--------------------

0=0

This is always true, which means there are infinite solutions.  This means the system is consistent.

3c  Add the two equations together.

6x+y =1

-6x-4y = -4

------------------

-3y = -3

Divide by -3

y = -1

We can solve for x

6x -3 = 1

Add 3 to each side

6x = 4

x = 4/6 = 2/3

There is one solution, which means the system is consistent