Question 186588This question is from textbook saxon algebra 2
: Solve the system of equations.
2x+y+z=9
-2x+3y+z=5
3x-y+2z=10
This question is from textbook saxon algebra 2
Answer by uday1435(57)   (Show Source):
You can put this solution on YOUR website! There are several methods to solve these equations. Matrix method, Cramers rule etc. Since I do not have the book mentioned, I shall solve it directly by manipulating the equations. Let us number these equations as
2x+y+z=9 (1)
-2x+3y+z=5 (2)
3x-y+2z=10 (3)
Eqn(1) eqn(2) gives
4x -2y = 4 let this be eqn(4)
Multiplying eqn(2) by 2 we get
4x + 2y + 2z = 18 Now subtract eqn(3) from this
3x y + 2z = 10
x + 3y = 8 let this be eqn (5)
Now multiply eqn (5) by 4 and subtract eqn (4) from it
4x + 12 y = 32 That is 4 x Eqn(5)
4x - 2y = 4 rewrote eqn 4 to subtract
14 y = 28 after subtraction
y = 2
Plug-in the value of y in eqn (5)
That is x + 3(2) = 8, ie. x + 6 = 8, so x = 2
Now plug in these values in eqn (1)
2(2) + (2) + z = 9
4+2+z =9; 6+z =9 so z= 9-6 =3. Therefore x = 2, y= 2 and z = 3 are the solutions.
|
|
|
