Step 1: Rearrange the equation √x +2y^2 = 15 to get x = (15 - 2y^2)^2.
Step 2: Substitute x = (15 - 2y^2)^2 in the equation √4x - 4y^2=6.
Step 3: Simplify the equation to get 4(15 - 2y^2)^2 - 4y^2 = 6.
Step 4: Solve for y^2 by rearranging the equation to get y^2 = (6 + 4(15 - 2y^2)^2)/8.
Step 5: Substitute y^2 = (6 + 4(15 - 2y^2)^2)/8 in the equation x = (15 - 2y^2)^2.
Step 6: Solve for x by rearranging the equation to get x = (15 - (6 + 4(15 - 2y^2)^2)/4)^2.
Step 7: Substitute y^2 = (6 + 4(15 - 2y^2)^2)/8 in the equation x = (15 - (6 + 4(15 - 2y^2)^2)/4)^2.
Step 8: Simplify the equation to get x = (15 - (6 + 60 - 8y^