Question

Solve

a. x + y + z = 2, x – y + z = 3, x + y + 2z = 0

b. 5x + y – 2z = 2, x + 2y + 3z = 2, 2x – y = 3

Answer #1

**a**.

**x+y+z = 2 .....(1)**

**x-y+z = 3 .......(2)**

**x+y+2z = 0 .....(3)**

add equation 1st and 2nd and 2nd and 3rd you will get

**2x+2z = 5 ....(4)**

**2x+3z = 3 ....(5)**

subtracting equation 4 from 5 you will get

**z = -2**

now put the value of z in equation 4 you will get

**x = 9/2**

now put value of x and z into equation 1 so you will get

**y = -1/2**

**so,**

**( 9/2 , -1/2 , -2) answer.**

**b.**

**5x+y-2z = 2 .....(1)**

**x+2y+3z = 2 ....(2)**

**2x-y = 3 ......(3)**

multiply equation 1 by 3 and equation 2 by 2 and then add equation 1 and 2 you will get

**17x+7y = 10 .....(4)**

by equation (3) and (4)

17x+7(2x-3) = 10

31x = 31

**x = 1**

now from equation 3

you will get

**y = -1**

now, from equation 1

**z = 1**

**so**

**(1,-1,1) answer.**

Solve each system by elimination.
1) -x-5y-5z=2
4x-5y+4z=19
x+5y-z=-20
2) -4x-5y-z=18
-2x-5y-2z=12
-2x+5y+2z=4
3) -x-5y+z=17
-5x-5y+5z=5
2x+5y-3z=-10
4) 4x+4y+z=24
2x-4y+z=0
5x-4y-5z=12
5) 4r-4s+4t=-4
4r+s-2t=5
-3r-3s-4t=-16
6) x-6y+4z=-12
x+y-4z=12
2x+2y+5z=-15

1. Solve the following system of equations by the elimination
method:
2x+y-z=7
x+2y+z=8
x-2y+3z=2
2. Solve the following system of equations by using row
operations on a matrix:
2x+y-z=7
x+2y+z=8
x-2y+3z=2

Use
Gaussian Elimination to solve and show all steps:
1. (x+4y=6)
(1/2x+1/3y=1/2)
2. (x-2y+3z=7)
(-3x+y+2z=-5)
(2x+2y+z=3)

Solve each system of equations
x-2y+3z=7
2x+y+z=4
-3x+2y-2z=-10

Solve the system using 3x3
3x-2y+z=2
5x+y-2z=1
4x-3y+3z=7

Use the technique developed in this section to solve the
minimization problem.
Minimize
C = x − 7y
+ z
subject to
x
−
2y
+
3z
≤
10
2x
+
y
−
2z
≤
15
2x
+
y
+
3z
≤
20
x ≥ 0, y ≥ 0,
z ≥ 0
The minimum is C =
at (x, y,
z) =

Minimize
C = x − 8y
+ z
subject to
x
−
2y
+
3z
≤
20
2x
+
y
−
2z
≤
30
2x
+
y
+
3z
≤
40
x ≥ 0, y ≥ 0,
z ≥ 0

Use the simplex method to solve the linear programming
problem.
Maximize
P = x + 2y + 3z
subject to
2x
+
y
+
z
≤
14
3x
+
2y
+
4z
≤
24
2x
+
5y
−
2z
≤
10
x ≥ 0, y ≥ 0, z ≥ 0
The maximum is P =
at
(x, y, z) =
( )
.

elementary linear algebra
Solve the system.
x+y+z=1
x+y-2z=3
2x+y+z=2

Solve the system of equations using an inverse matrix
-4x-2y+z= 6
-x-y-2z= -3
2x+3y-z= -4
Choose one:
a. (-1, 0, -2)
b. (1, 0, -2)
c. (1, 0, 2)
d. (-1, 0, 2)

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