AskSia

Plus

Question 1 Find all solutions (if any) to the following systems of linear equat...

Sep 24, 2024

Solution by Steps

step 1

To solve the first system of equations:

x + y + 2z = -1

x - 2y + z = -5

3x + y + z = 3

, we find the values of

x

y

, and

z

. The solution is

x = 1

y = 2

, and

z = -2

step 2

For the second system of equations:

x + 2y - z = 0

2x + y + z = 0

5x + 7y + z = 0

, we find that the only solution is

x = 0

y = 0

, and

z = 0

Answer

The solutions are

(x, y, z) = (1, 2, -2)

for the first system and

(0, 0, 0)

for the second system.

Key Concept

Solving systems of linear equations involves finding values for the variables that satisfy all equations simultaneously.

Explanation

The first system has a unique solution, while the second system has only the trivial solution. This illustrates the different types of solutions that can exist in linear algebra.