Solve each system of equations. Let z be the parameter.
x + 2y + 3z = 11
2x – y + z = 2
2007-09-11 10:51:29 · 10 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
There are 3 unknowns viz x , y and z.
There should therefore be 3 equations.
2007-09-14 08:59:09 · answer #1 · answered by Como 7 · 1⤊ 0⤋
What you want to do is to solve x & y so they only depend on z.
(1) x + 2y + 3z = 11
(2) 2x - y + z = 2
From (1) slove x by moving the rest from left to right
(3) x = 11 -2y -3z
Use (3) in to replace x in (2) to get the y
2(11 - 2y - 3z) - y + z = 2 => 22 - 5y - 5z = 2 =>
20 - 5z = 5y => y = 4 - z (5)
(5) in (3) gives
x = 11 - 2(4 - z) - 3z = 3 - z
So the answer is
x = 3 - z (6)
y = 4 - z (7)
where both x & y only depends on parameter z as asked.
To verify that the answer is correct just insert (6) & (7) in (1) and (2) to see that both sides stay equal.
(6), (7) => (1)
(3 - z) + 2(4 - z) + 3z = 11 -3z + 3z = 11
(6), (7) => (2)
2(3 - z) -(4 - z) + z = 2 -2z +z + z = 2
2007-09-11 11:20:58 · answer #2 · answered by snowboll_2000 1 · 0⤊ 1⤋
It's been a long time, but 3 parameters and two equations can only give you a relation between x and y without telling you what x and y really are.
A good question to bring to your Philosophy teacher in case it's not the same as the Math teacher ;-)
2007-09-11 10:57:56 · answer #3 · answered by Anonymous · 0⤊ 0⤋
for 2(x + 2y + 3z )= 2(11) into A:2x+4y+6z=22:let us name B:2x – y + z = 2,
and z is the parameter,
So ,A-B=5y-5z=10,
so,y-z=5.
y=5+z,
put y=5+z intoA equation,
x+2(5+z)+3z=11,
so, x=11-10-5z
=1-5z.
2007-09-11 11:06:09 · answer #4 · answered by Hang 3 · 0⤊ 0⤋
Oh my gosh, I used to know how to do this, and now I've forgotten! *cries*
But, I THINK maybe you're supposed to rearrange each equation to equal a particular variable, and then solve for that variable. Solve for at least two variables I think, and once you've done that you can substitute the answers into either equation and get the final answer. Sorry I can't help you any more than that =/
2007-09-11 11:05:13 · answer #5 · answered by oh geez 6 · 0⤊ 1⤋
Solve the second equation for y, and substitute the result into the first equation. That's all there is to it.
2007-09-11 10:57:37 · answer #6 · answered by Anonymous · 0⤊ 1⤋
I used to know this. How embarrasing
2007-09-11 10:56:06 · answer #7 · answered by Vegas Mike 3 · 1⤊ 0⤋
huh I'm sorry but ur on your own sister cuz i have no idea what that is
2007-09-11 10:56:33 · answer #8 · answered by Anonymous · 1⤊ 0⤋
Each one individually? or together?
2007-09-11 10:57:06 · answer #9 · answered by x3_chubi 3 · 1⤊ 0⤋
y don't u pay attention in class?
2007-09-11 10:56:20 · answer #10 · answered by jennifer 4 · 1⤊ 0⤋