Question

I had problems using the substitution method, to solve this system...checked my answer key, it said no solution was to be found for this system, no wonder. :P Just wanting a specific explanation of why this system does not have a solution. See system below..
3x = 2y - 4
6x - 4y = - 4

Answer 1

one eqn is a multiple of the other

Answer 2

eqn 1: 3x = 2y-4
eqn2: 6x = 4y-4

Answer 3

nah thats actually wrong

Answer 4

you didnt copy the equations correctly

Answer 5

I did copy them right...I'm wanting to know why the answer key says there is no solution to this system..

Answer 6

I took one of the equations to use the substitution method. The equation I took is:

6x-4y=-4
6x+4=4y Rearranging this equation you get:

4y=6x+4
y=(6x+4)/4=6x/4+4/4
y=(3/2)(x)+1 Substitute this y value into the other equation and you get:

3x=2y-4
3x=(2)[(3/2)(x)+1]-4
3x=3x+2-4
3x=3x-2
3x-3x=-2
0=-2 This is not true : 0 does not equal -2

Therefore, there is no solution to this system

Answer 7

There is a geometrical explanation to this result. If we look at the the system of equations, they can be re-arranged as
1. y=(3/2)x + 2 and
2. y=(3/2)x + 1 , which are equation of lines in the slope-intercept form y=mx+c.
Notice that slope of both the lines are same, which makes the two lines parallel and both are on the same side of Y-axis. Parallel lines do not intersect anywhere, so there can be no (x,y) which satisfies both the lines simultaneously. Hence, no solution.
Look at the attachment.