Problem 3: Consider the following pair of algebraic equations: 10x + 3y = 3 r? -exp(y) = 2 1) Solve the first equation for x, and substitute into the second equation. Plot the resulting fl) and determine the root graphically. Determine the corresponding x value 2) Using the Generalized Newton's method, solve this system of equations using both of the original equations (use an initial guess x = 0, y=0). 3) Using the Matlab function 'fsolve' Problem 4: Recall the definition of a two-dimensional ellipse. 1=1 X-X y-y ( 9-6 ( Where the center of the ellipse is the point (x, y) and the radii in each direction are given by X, and yr. Now consider the intersection of two ellipses 1"** 1-(872)+(93) 1-(82)+(1959 1= 1) Sketch the two ellipses and estimate the two points of intersection. 2) Write a MATLAB code to use Newton's method to find an intersection point. 3) Test the code of part 2, using a variety of initial conditions and comment on how the initial condition will influence which intersection point is found. 4) Identify two ellipses that do not intersect. Test your algorithm on this set of equations that have no solution. Problem 4: Recall the definition of a two-dimensional ellipse. 1=1 X-X y-y ( 9-6 ( Where the center of the ellipse is the point (x, y) and the radii in each direction are given by X, and yr. Now consider the intersection of two ellipses 1"** 1-(872)+(93) 1-(82)+(1959 1= 1) Sketch the two ellipses and estimate the two points of intersection. 2) Write a MATLAB code to use Newton's method to find an intersection point. 3) Test the code of part 2, using a variety of initial conditions and comment on how the initial condition will influence which intersection point is found. 4) Identify two ellipses that do not intersect. Test your algorithm on this set of equations that have no solution