If the graphs of two linear equations in a system have different slopes, the system _____has exactly one solution.
Is it Always, sometimes or never.
Thanks
2007-07-01 04:56:19 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
always
2007-07-01 04:59:06 · answer #1 · answered by foooooood 3 · 0⤊ 0⤋
Think about this. If two linear equations have different slopes, they MUST intersect somewhere. The intersection is always at a point.
How can the intersection be at more than 1 point unless the two lines have the same slope and same intercept (which means they are the same line anyway)?
The answer has to be "always"
2007-07-01 05:01:59 · answer #2 · answered by GTB 7 · 0⤊ 0⤋
always. the solution is that point where the 2 slopes intersect (cross) think of drawing an X on a piece of graph paper. the only point that the 2 lines have in common is where they meet.
2007-07-01 05:04:55 · answer #3 · answered by New rider-- again 3 · 0⤊ 0⤋
They will intersect at only 1 point, but well there might be two different value for x and y.
For example
2x+4y=6
6x+2y=10
Multiply top equation by 3
6x+12y=18
6x+2y=10
10y=8
y=8/10
Now go back to the earlier equations and multiply the bottom equation by 2.
2x+4y=6
12x+4y=20
Subtract
-10x=-14
x=7/5
So x and y are different, but they mean just 1 point.
2007-07-01 05:03:34 · answer #4 · answered by UnknownD 6 · 0⤊ 0⤋