Question

Solve. You will find a system with an infinite number of solutions, with no solution, or with a unique solution. (Enter your answers as a comma-separated list. If there are infinitely many solutions, enter a parametric solution using t and s as the parameters. If there is no solution, enter NONE.)

3x + 6y − 15z = 36
-4x − 8y + 20z = -48
(x,y,z) = _____

Answer 1

The given system of equations has an infinite number of solutions and can be represented parametrically.

Step-by-step explanation:

The given system of equations is:

3x + 6y - 15z = 36

-4x - 8y + 20z = -48

We can solve this system using the method of elimination. By multiplying the first equation by 2 and the second equation by 3, we can eliminate the variable x:

6x + 12y - 30z = 72

-12x - 24y + 60z = -144

Adding these two equations, we get:

-6y + 30z = -72

Simplifying and rearranging, we have:

-3y + 15z = -36

Dividing this equation by -3, we get:

y - 5z = 12

This equation is not dependent on x, meaning we can choose any value for x. Therefore, this system has an infinite number of solutions and the solution can be represented parametrically as:

x = t, y = 12 + 5t, z = t