Graph each system. Tell whether the system has no solution, one solution, or infinitely many solutions.
y = 5x – 4
y = 5x – 5
no solutions
one solution
infinitely many solutions
three solutions
2007-05-03 04:52:39 · 8 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
y = 5x - 4- - - - - - -Equation 1
y = 5x - 5- - - - - - -Equation 2
- - - - - - - -
Convert equation 2 to standard form
y = 5x - 5
- 5x + y = 5x - 5 - 5x
- 5x + y = - 5. . .Standard form equation 2
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insert the y value equation 1 into Standard form equation 2
- 5x + y = - 5
- 5x + 5x - 4 = - 5
The coefficients and variables cancell. No solution
- - - - - - - - - - -s-
2007-05-03 05:48:34 · answer #1 · answered by SAMUEL D 7 · 1⤊ 0⤋
First, I haven't found a way to get graphs onto this site. So I can't show you a graph.
There is only one "system" of equations. graphing each of the equations, were it possible here, would show if there was a solution.
However:
y = 5x - 4 is a line with a slope of 5 crossing the y axis at (0,-4)
7 = 5x - 5 is a line with a slope of 5 crossing the y axis at (0,-5).
A solution to a system of equations is the set of points that satisfy all the equations in the system.
Since the lines generated by the two equations have the same slope, the lines are parallel. Parallel lines either have all points in common, or they have none.
Since they do not cross the y axis at the same point, they do not have all points in common. So they have none. Therefore, the system of equations has no solution.
2007-05-03 12:14:44 · answer #2 · answered by gugliamo00 7 · 0⤊ 0⤋
I can't show the graph here, but these lines
will be parallel, because they have the same slope,
namely 5.
There is no solution to this system:
Indeed, since both equations equal y, we have
5x-4 = 5x -5
or -4 = -5,
which is impossible.
2007-05-03 12:01:34 · answer #3 · answered by steiner1745 7 · 0⤊ 0⤋
Remember the equation for a line:
y = mx + b
where
m = slope
b = y-intercept
Both the equations have the same slope (m is same), but have different y-intercepts (b is different).
Because the y-intercept is different we know they are not the same line.
Because the slope is the same, the lines are parallel.
Parellel lines NEVER intersect, so the answer is: no solution.
2007-05-03 12:03:19 · answer #4 · answered by Sam 2 · 0⤊ 0⤋
No solution because the lines are parallel (both have a slope of 5) and are not the same line because they have different y-intercepts.
2007-05-03 11:58:08 · answer #5 · answered by Rapptastic 1 · 0⤊ 0⤋
Two parallel lines
Each has infinitely many solutions
2007-05-03 11:57:24 · answer #6 · answered by MamaMia © 7 · 0⤊ 1⤋
Both equations have infinite solutions.
2007-05-03 12:00:27 · answer #7 · answered by dwinbaycity 5 · 0⤊ 1⤋
no solution cause a1/a2 is not= to b1/b2
2007-05-03 12:01:45 · answer #8 · answered by cool d 1 · 0⤊ 0⤋