2006-12-23 12:40:31 · 19 answers · asked by Little Britches 3 in Science & Mathematics ➔ Mathematics
Solutions come from the intersections of graphs. Lines that are parallel never intersect so they don't have any solutions.
2006-12-23 12:49:46 · answer #1 · answered by knock knock 3 · 4⤊ 0⤋
Rule of thumb: two lines are parallel if they have the same slope.
Second rule of thumb: Two parallel lines are either going to have no solution (i.e. they're parallel so they don't cross), or ALL solutions (they are exactly the same line).
Take these two lines:
x - y + 1 = 0
3x - 3y + 3 = 0
Let's put these both in y-intercept from.
x - y + 1 = 0
-y = -x - 1. Multiplying both sides by -1, we get
y = x + 1
3x - 3y + 3 = 0
-3y = -3x - 3. Divide both sides by -3, and we get
y = x + 1
We have the exact same lines, and when we try and solve for one variable x, we get
x + 1 = x + 1, or 0 = 0 (which is a true statement, so the answer is all real numbers).
Just wanted to add this fact that, since everybody responded there are no solutions, that the possibility of having ALL solutions for parallel lines is there too.
2006-12-23 13:46:19 · answer #2 · answered by Puggy 7 · 1⤊ 0⤋
It has none.
Add 3x to each equation
Then y + 3x =8
and
y + 3x = 9.
If there were a solution, this would give 8 = 9,
which is nonsense.
2006-12-23 12:56:52 · answer #3 · answered by steiner1745 7 · 3⤊ 0⤋
None, here's the reason why:
-3x+8=-3x+9
Add 3x from both sides:
0x+8=9
0x=1
Check:
-3(0)+8=1
8â 1
-3(0)+9=1
9â 1
Another way you can find out is by graphing them on graphing paper or you can put this into the graphing calculator. If the graphs do not intersect, then there is no solution.
2006-12-23 12:50:25 · answer #4 · answered by Anonymous · 3⤊ 0⤋
Zero. These are parallel lines
y = -3x+8
y= -3x + 9? subtract
0=-1
2006-12-23 12:51:57 · answer #5 · answered by mu_do_in 3 · 4⤊ 0⤋
Do you see -3 in BOTH equations? The -3 stands in the place of m for y = mx + b and m = THE SLOPE.
This means that BOTH equations have the SAME SLOPE = PARALLEL LINES.
Since parallel lines DO NOT MEET, there is no solution.
In order to have a solution, the lines MUST MEET or TOUCH but in your sample question, the lines NEVER meet or touch and so, there is NOT SOLUTION.
Guido
2006-12-23 13:50:44 · answer #6 · answered by Anonymous · 1⤊ 0⤋
Zero!! Yay!! Parallel lines never cross which is what a solutions to a system of equations is, a point of intersection. Since these two lines have the same slope (-3) and therefore never intersect, there are no solutions.
2006-12-23 12:49:48 · answer #7 · answered by Mike J 3 · 4⤊ 0⤋
There are none.
But in general, when you have an N amount of variables, you need the same number of equations with DIFFERENT coefficients for at least one of the variables, so you can obtain a numerical solution.
Say you have three variables to solve for across two equations, you'll be going around in a circle, because you'll end up with having one variable having in terms of another and then obtaining a similar answer with that variable being in therms of the former.
2006-12-23 17:59:47 · answer #8 · answered by ariotinlondon 2 · 2⤊ 0⤋
y = -3x + 8
y = -3x + 9
-3x + 8 = -3x + 9
0x = 1
x = Undefined
No Solution
2006-12-23 13:34:01 · answer #9 · answered by Sherman81 6 · 1⤊ 0⤋
There are no solutions for this system of eqns.
The reason why is b/c the two lines are parallel as they both have the same slope, but different y-intercepts.
2006-12-23 12:42:38 · answer #10 · answered by AibohphobiA 4 · 6⤊ 0⤋