Question

Use the Newton-Raphson method to determine the solution of the simultaneous nonlinear equations: y=−x2+x+0.75 y+5xy=x2 Use the initial guesses of x = y = 1.2, and iterate until the 4th iteration. (Round the final answers to five decimal places.) The values of x and y are as follows: iterationxy01.21.21 0.0290321.39412 3 0.239294

Answer 1

Answer:

Step-by-step explanation:

Let's solve for y.

−x2+x+0.75y+5xy=x2

Step 1: Add x^2 to both sides.

−x2+5xy+x+0.75y+x2=x2+x2

5xy+x+0.75y=2x2

Step 2: Add -x to both sides.

5xy+x+0.75y+−x=2x2+−x

5xy+0.75y=2x2−x

Step 3: Factor out variable y.

y(5x+0.75)=2x2−x

Step 4: Divide both sides by 5x+0.75.

y(5x+0.75)

5x+0.75

=

2x2−x

5x+0.75

y=

2x2−x

5x+0.75

Answer:

y=

2x2−x

5x+0.75