Answer:
c = - 4
Explanation:
Nothing else matters except that the number associated with the y value in equation one = 1 and the number in front of x is known in equation 1. Then we'll get around to looking at c
Add 2y to both sides of equation 1 (the top equation)
3x - 2y + 2y = 3 + 2y
3x = 2y + 3
Now divide both sides of the equation by 2
3x/2 = y + 3/2
What's in front of x? It is (3/2)
So divide both sides of 6x + cy = 4 by c
6x/c + y = 4/c
Now put 6x/c on the right hand side so y is by itself.
y = -6x/c + 4/c
What do you have to do now?
You must equate -6x/c = 3/2x
Why?
The slopes have to be the same so the lines are parallel and never cross. That will give no solutions.
-6x/c = 3x / 2 Divide both sides by x
-6/c = 3/2 Cross multiply
3c = - 6 * 2 Combine
3c = - 12 Divide by 3
c = - 12/3
c = - 4