Question

What is the value of the x variable in the solution to the following system of equations?

2x − 3y = 3
5x − 4y = 4

Answer 1

both equations have different slopes so they cannot be parallel lines

Answer 2

parallel lines will have the same slope

Answer 3

You have only one "system of linear equations" here (not 2 or 3 or more). Your job is to determine whether or not you can solve this "system of linear equations."

If your two equations represent 2 lines, and the lines have the same slope, then your lines never intersect, and thus you have no solution. "no x value" is incorrect; there'd be no y value either. Better to say, "no solution."

Answer 4

the easiest way to visualise a straight line equation is to put it in slope intercept form

y=mx+b

your equations can be rewritten as
y = 2/3 x-1
and
y= 5/4 x -1

the value of m tells you the slope

IF the 2 lines have different slope then they MUST intersect at one point only, and hence have one solution to the 'system'

Answer 5

so x is -1

Answer 6

how did you derive that?

if oyu show some working you can be guided more easily

Answer 7

How does it make sense to ask "so it's x=-1?"

Again, two parallel lines do NOT intersect, and thus the system has NO solution. It is very important that you understand these principles.

Answer 8

btw x=-1 is not correct

Answer 9

What im trying to ask is if there is an x value and what it is. I thought the system was parallel therefore having no solution, x, or y value.

Answer 10

IF the 2 lines have different slope then THEY ARE NOT PARALLEL and they MUST intersect at one point only, and hence have one solution to the 'system'

Answer 11

You have confused the question by putting 'parallel' in the question

please post it exactly as you have it

Answer 12

that was the original question, i just updated it.

Answer 13

y=mx+b
the value of m tells you the slope

your equations can be rewritten as
y = 2/3 x-1
and
y= 5/4 x -1


So WHAT is th e slope of each line - and are they equal?

Answer 14

OK so now you are not starting with the assumption that they are parallel

SO can you answer my question in my last post

Answer 15

the slopes are different. so its not parallel

Answer 16

correct

now - the b value tells you where the lines cross the y axis

where does each line cross?

Answer 17

they both have the same y - intercept yea got it

Answer 18

so where do they intersect each other?

Answer 19

-1

Answer 20

OK good but you need (x,y) point

what is the x value at the y intercept?

Answer 21

x=0 y=-1

Answer 22

OK so you have your answer...