Suppose f(x,y)=xy(1−10x−4y)f(x,y)=xy(1−10x−4y). f(x,y)f(x,y) has 4 critical points. List them in increasing lexographic order. By that we mean that (x, y) comes before (z, w) if x<zx<z or if x=zx=z and y<wy<w. Also, determine whether the critical point a local maximum, a local minimim, or a saddle point. First point (____________,__________) Classification: Second point(__________,__________) Classification: Third point (___________,_________) Classification: Fourth point (__________,_________) Classification:
Solve the system by the substitution method {y=-4× +1 {3x-4y=15
(a) 3x-4y 8 Solve for y.
6. (15 pts) For the linear system 3x + 2y + 10x = -6 3 + 2z = y+2z = 3 3+ 4y + 10% = 8 a) Use your calculator to place the augmented matrix in RREF and write it here. 3 2 10 -6 i 470 - 4 3 8 b) Find the general solution to the linear system, written as either the vector equation of a line or the vector equation of a plane.
Homogenous equation 1. (2x – y) y = 4y – 3x, y(0) = 2
2. x+4y= 14 2x - y=1 x=2, y=3 3. 5x + 3y = 1 3x + 4y = -6 x=2, y=-3 | 4, 2y- 6x =7 3x - y=9 No solution/Parallel lines
x-4 7. Pax- 8. 4x-y=3 (3x +2y=-18 10. 1, y=2x-4 12.13x+4y-8 r=-4
Solve x′ =2x+y, x(0)=1 y′ =3x+4y, y(0)=0
Solve the systems of equations by substitution #11 2x-y-2 3x+4y-6 Solve each system by elimination or by any convenient method #13 a) 3x+4y-1 2x-3y-12 b) -4x+3y--!5 3x-2y-4
of equation Solve the system 3x + 4y = -14 5x+7 y = -25