Find three distinct solutions of the equation x1 + 2x2 = 4. Find a parametric representation of the solution set.

Sure, let's solve the equation step by step.

1. The given equation is x1 + 2x2 = 4. This is a linear equation with two variables x1 and x2.

2. To find distinct solutions, we can choose arbitrary values for one variable and solve for the other.

Solution 1: Let's choose x1 = 0. Substituting x1 = 0 into the equation, we get: 0 + 2x2 = 4 Solving for x2, we get x2 = 4/2 = 2. So, one solution is (x1, x2) = (0, 2).

Solution 2: Let's choose x1 = 2. Substituting x1 = 2 into the equation, we get: 2 + 2x2 = 4 Solving for x2, we get x2 = (4-2)/2 = 1. So, another solution is (x1, x2) = (2, 1).

Solution 3: Let's choose x1 = 4. Substituting x1 = 4 into the equation, we get: 4 + 2x2 = 4 Solving for x2, we get x2 = (4-4)/2 = 0. So, another solution is (x1, x2) = (4, 0).

3. Now, let's find a parametric representation of the solution set.

We can rewrite the given equation as x1 = 4 - 2x2.

Let x2 = t (where t is a parameter). Then, x1 = 4 - 2t.

So, the parametric representation of the solution set is (x1, x2) = (4 - 2t, t), where t is any real number.