# 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

 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