Consider the homogeneous system (a) If x x 0 and y y 0 is a solution and k is a real number, then show that x kx 0 and y ky 0 is also a solution (b) If x x 1 , y y 1 and x x 2 , y y 2 are both solutions, then show that x x 1 x 2 , y y 1 y 2 is a solution ax by 0 cx dy 0 ...

a If x 0 y 0 is a solution then it follows that ...

Consider the homogeneous system (a) If x = x 0 and y = y 0 is a

Question:

Consider the homogeneous system

(a) If x = x₀ and y = y₀ is a solution and k is a real number, then show that x = kx₀ and y = ky₀ is also a solution.(b) If x = x₁, y = y₁ and x = x₂, y = y₂ are both solutions, then show that x = x₁ + x₂, y = y₁ + y₂ is a solution.