logo for solving-math-problems.com
leftimage for solving-math-problems.com

NONLINEAR SYSTEM HELP











































A)USe any valid method to solve the following system.

{2x-3y+z=10
3x-y-2x=1
x+2y+4z=12

B) Solve the following nonlinear system.

{2x+y+3=0
(x)^2+(y)^2=5

Comments for NONLINEAR SYSTEM HELP

Click here to add your own comments

Apr 20, 2011
Solve Non-Linear System of Equations
by: Staff


The question:

A) Use any valid method to solve the following system.

2x-3y+z=10
3x-y-2x=1
x+2y+4z=12

B) Solve the following nonlinear system.

2x+y+3=0
(x)^2+(y)^2=5

The answer:

A) Use any valid method to solve the following system.

2x - 3y + z = 10
3x - y - 2x = 1
x + 2y + 4z =12

2 x - 3 y + z = 10
x - y = 1
x + 2 y + 4 z = 12

x = y + 1
2 x - 3 y + z = 10
x + 2 y + 4 z = 12

x = y + 1
( 2 y + 2) - 3 y + z = 10
x + 2 y + 4 z = 12

x = y + 1
2 y + 2 - 3 y + z = 10
x + 2 y + 4 z = 12

x = y + 1
- y + z + 2 = 10
x + 2 y + 4 z = 12

x = y + 1
- y = - z + 8
x + 2 y + 4 z = 12

x = y + 1
y = z - 8
x + 2 y + 4 z = 12

x = y + 1
y = z - 8
( y + 1) + 2 y + 4 z = 12

x = y + 1
y = z - 8
( ( z - 8) + 1) + 2 ( z - 8) + 4 z = 12

x = y + 1
y = z - 8
( z - 8 + 1) + 2 ( z - 8) + 4 z = 12

x = y + 1
y = z - 8
( z - 7) + 2 ( z - 8) + 4 z = 12

x = y + 1
y = z - 8
z - 7 + 2 ( z - 8) + 4 z = 12

x = y + 1
y = z - 8
5 z + 2 ( z - 8) - 7 = 12

x = y + 1
y = z - 8
5 z + ( 2 z - 2 * 8) - 7 = 12

x = y + 1
y = z - 8
5 z + ( 2 z - 16) - 7 = 12

x = y + 1
y = z - 8
5 z + 2 z - 16 - 7 = 12

x = y + 1
y = z - 8
7 z - 23 = 12

x = y + 1
y = z - 8
7 z = 35


x = y + 1
y = z - 8
7 z/7=35/7

x = y + 1
y = z - 8
z = 5(7/7)

x = y + 1
y = z - 8
z = 5

x = y + 1
y = 5 - 8
z = 5

x = - 3 + 1
y = - 3
z = 5

the final answer is:

x = - 2
y = - 3
z = 5



Check the work. Substitute -2 for x, -3 for y, and 5 for z in the original three equations.

Verify solutions for x, y, and z in first equation

2x - 3y + z = 10
2(-2) - 3(-3) + 5 = 10

Verify solutions for x, y, and z in second equation

3x - y - 2x = 1
3(-2) - 1(-3) – 2(-2) = 1

Verify solutions for x, y, and z in second equation

x + 2y + 4z =12
-2 + 2(-3) + 4(5) = 12



B) Solve the following nonlinear system.

2x + y + 3 = 0
x² + y² = 5

2x + y + 3 = 0
y = -2x - 3

x² + y² = 5

x² + (-2x – 3)² = 5


x² + [(-2x)² + 2(-2x)(- 3) +(- 3)²] = 5

x² + [(2x)² + 2*2x*3 + 3²] = 5

x² + (2² * x² + 2*2*3*x + 9) = 5

x² + (4x² + 12x + 9) = 5

x² + 4x² + 12x + 9 = 5

5x² + 12x + 9 = 5

5x² + 12x + 4 = 0

x = [-12 ± sqrt(12² - 4*5*4)]/(2*5)

x1 = -0.4

x2 = -2


y = -2x - 3

y1 = -2*(-0.4) - 3

y1 = -2.2


y2 = -2*(-2) - 3

y2 = 1


the final answer is

x1 = -0.4; y1 = -2.2

x2 = -2; y2 = 1


Check the work. Substitute x and y in the original two equations.

Verify solutions for x1 and y1 in the first equation

2x + y + 3 = 0
2(-0.4) + (-2.2) + 3 = 0, OK

Verify solutions for x1 and y1 in the second equation

x² + y² = 5
(-0.4)² + (-2.2)² = 5, OK

Verify solutions for x2 and y2 in the first equation

2x + y + 3 = 0
2(-2) + (1) + 3 = 0, OK

Verify solutions for x2 and y2 in the second equation

x² + y² = 5
(-2)² + 1² = 5, OK









Thanks for writing.


Staff
www.solving-math-problems.com

Click here to add your own comments

Join in and write your own page! It's easy to do. How? Simply click here to return to Math Questions & Comments - 01.



Copyright © 2008-2015. All rights reserved. Solving-Math-Problems.com