questions below:

a. Solve the system u = 2x + 3y, v= x + 5y for x and y in terms of u and v. Then find the value of the Jacobian a(x,y) a(u,v) b. Find the image under the transformation u = 2x + 3y, v= x + 5y of the triangular region in the xy-plane bounded by the x-axis, the y-axis, and the line x + y = 1. Sketch the transformed image in the uv-plane. a. x = ], y= The Jacobian is. b. Choose the correct sketch of the transformed region in the uv-plane below. O A. OB. O C. OD. AV uEvaluate the integral directly by integration with respect to x and y. 3 x = (y/6) +1 6x - y 6 -dxdy 0 X=y/6 Integrate with respect to x. 3 X= (y/6) +1 Co 6x - y dxdy 6 1 ()dy 0 X =y/6 0 (Simplify your answer.) Integrate the result with respect to y. 3 X= (y/6) +1 6x - y dxdy = 6 0 x=y/6 (Simplify your answer.)Evaluate the integral by integrating with respect to x, y, and z. X = = + 1 16 2 3 SSS 3 x - y + dx dy dz 0 0 X= Integrate with respect to x. X = ~ +1 16 2 3 16 2 SSS 3x - y 3 + dx dy dz = SS( dy dz 0 X= w/ * 0 0 Integrate the result with respect to y. X = = + 1 16 2 16 0 0 X= w/ * Integrate the result with respect to z. X = ~ +1 16 2 3 SS. 3 x - y 3 dx dy dz = 0 0 X= = (Simplify your answer.)