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
