How to Solve nonlinear system by newton method?

I need someone to explain how to: 1-Solve a system of two linear equations by the graphing method. 2-Solving a system of two linear equations by the substitution method. 3-Solving a system of two linear equations by the addition( elimination) method

• Answer:

  Let's say our two simple equations are 2X + Y = 0 and 4X + Y = 6 1. Graphing Simply draw the graphs of the two equations to determine the coordinates of the single intersecting point. That will be the shared solution to the two simultaneous equations. That is, it will be the answer to both equations at the same time (the solution that makes them "simultaneous"). I'll leave this one for you to do. (See if you can do it before you read the rest of this response.) 2. Substitution Solve either one of the equations for one variable in terms of the other. For example, take our first simple equation of 2X + Y = 0. In that case, 2X = -Y, or X = -Y/2. Now, with our other equation of 4X + Y = 6, then we simply substitute our new value of X: 4 * (-Y/2) + Y = 6 -4Y/2 + Y = 6 -2Y + Y = 6 -Y = 6 Y = -6 If Y = -6, then 2X + Y = 0, and 2X -6 = 0, so 2X = 6 and X = 3 3. Elimination Set up the equations one on top of the other and see what you have to do (to both sides of an equation, remember!) to have an "equal term" that you can subtract, one from the other. Let's see: 2X + Y = 0 and 4X + Y = 6 Well, this is easy; we already have a single "Y" term in both equations! So just subtract the second equation from the first one: 2X - 4X + Y - Y = 0 - 6 (We could have subtracted the first from the second, if we wanted: 4X - 2X + Y - Y = 6 - 0. That actually gives us the same equation, but without the extra - sign on both sides.) Solving the first or second equation: 4X - 2X = 6 2X = 3 And solving for Y in our first equation: 2X + Y = 0 2 * 3 + Y = 0 6 + Y = 0 Y = -6 Does this match your graph from the first section of the answer?