Systems of Equations & Solutions

Question

For each of the following systems of equations, state if the system has a unique solution, an infinite number of solutions, or is inconsistent (no solutions). If the system has a unique solution, exhibit the solution. If the system has an infinite number of solutions, exhibit three different solutions.

x + y + z + w = 0

4x + 3y + 5z - w = -5

2x + 5y + 3z + 9w = 3

3x - 4y - 2z + 3w = 1

5x + 2y + 3z - 4w = 0

Answer 1

Use row operations to find the solutions to the system of linear equations.

You will need row operations for addition, subtraction, multiplication, division, and switching rows.

In this case, you will have 4 unique solutions.

x = 1, y = 2, z = -3, w = 0 → (1, 2, -3, 0)