Knowee
Questions
Features
Study Tools

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

Question

Find three distinct solutions of the equation

x_1 + 2x_2 = 4

Find a parametric representation of the solution set.

🧐 Not the exact question you are looking for?Go ask a question

Solution

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).

  1. 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.

This problem has been solved

Similar Questions

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

The ordered pairs for a linear graph are recorded in the table below.x –2 0 1 2y 4 0 –2 –4What is the algebraic equation for this table of values?

Given the equation has point of intersection with the x axis atQuestion 2Select one:a.x = -2 and x = 4b.x = 2 and x = -4c.x = 2 and x = 4d.x = -2 and x = -4

Draw the solution sets for the following two equations for $-3\leq x_1 \leq 3$: $$0 x_1 + 8 x_2 = -2 $$ and $$-1 x_1 + 6 x_2 = -2 $$

Solve each system of equations by graphing.y = 2x + 1y = -x + 1x + y = 4x + y = 2

1/1

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.