Question 1163638: Please help me solve this problem. I tried to do it all different ways and am completely stumped.
Solve the following system of equations for the unknown variables.
3x + 3y = 3
-3x - 2z = -11
y + z = -1
(NOTE: Show answer in the following format (#,#,#), using the parentheses in your answer. If not entered in this format, will be scored incorrect.)
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! your equations are:
3x + 3y = 3
-3x - 2z = -11
y + z = -1
solve for z in the third equation to get z = -y - 1
replace z in the second equation to get -3x - 2 * (-y-1) = -11.
simplify to get -3x + 2y + 2 = -11
subtract 2 from both sides of the equation to get -3x + 2y = -13
you can now solve the first 2 equations simultaneously.
they are:
3x + 3y = 3
-3x + 2y = -13
add the equations together to get:
5y = -10
solve for y to get y = -2
replace y with -2 in the first equation to get:
3x + 3y = 3 becomes 3x - 6 = 3
add 6 to both sides of that equation to get 3x = 9
solve for x to get x = 3
you now have x = 3 and y = -2
go back to the third equation and replace y with -2
y + z = -1 becomes -2 + z = -1
add 2 to both sides of that equation to get z = 1
you now have x = 3 and y = -2 and z = 1
go back to youor 3 original equations and replace x and y and z with their respective values to see if those equations are true.
3x + 3y = 3 becomes 3*3 - 3*2 = 3 which becomes 9 - 6 = 3 which becomes 3 = 3 which is true.
-3x - 2z = -11 becomes -3*3 - 2*1 = -11 which becomes -9 - 2 = -11 which becomes - 11 = -11 which is true.
y + z = -1 bcomes -2 + 1 = -1 which becomes -1 = -1 which is true.
it looks like x = 3, y = -2, z = 1 is your solution.
it can be shown in (x,y,z) format as (3,-2,1)
Answer by greenestamps(13203)  (Show Source):
You can put this solution on YOUR website!
There are always countless ways to solve a system of three linear equations in three unknowns.
If you are using a purely algebraic technique, the objective is to first eliminate one of the equations to get two equations in two unknowns. Then of course when you get to that point there are different ways of solving.
Here is what I see when I look at the three given equations: adding the first two equations eliminates x. So....
3x+3y=3; -3x-2z = -11 --> 3y-2z = -8
y+z = -1
For two equations in two unknowns, with the equations in this form, I prefer a solution by elimination.
(1) 3y-2z = -8
(2) y+z = -1
Multiply (2) by 2 and add to (1):
3y-2z = -8
2y+2z = -2
-----------
5y = -10
y = -2
Substitute y=-2 in (2) to find z = 1.
Substitute y=-2 in the first original equation to find x=3.
ANSWER: (x,y,z) = (3,-2,1)
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