Question

Identify the number of solutions of the system of linear equations

2+y+z=2
2x - 3y +z = 11
-3. + 2y – 2z = -13
A. No solution
B. exactly one solution
C. infinitely many solutions

Answer 1

The system of linear equations has infinitely many solutions.

Step-by-step explanation:

The given system of linear equations is:

2 + y + z = 2

2x - 3y + z = 11

-3 + 2y - 2z = -13

We can solve this system by using the method of elimination or substitution. Let's use the method of elimination:

Multiply the first equation by -2 and the second equation by 1:

-4 - 2y - 2z = -4

2x - 3y + z = 11

Adding these two equations, we get:

-2y - z = 7

2x - 3y + z = 11

Now, multiply the third equation by -2 and add it to the second equation:

2x - 3y + z = 11

-6 + 4y - 4z = 26

Adding these two equations, we get:

4y - 3z = 37

Now, multiply the first equation by 3 and add it to the third equation:

6 + 3y + 3z = 6

-3 + 2y - 2z = -13

Adding these two equations, we get:

3y + z = -7

Now we have the system of equations:

-2y - z = 7

4y - 3z = 37

3y + z = -7

By solving this system, we find that there are infinitely many solutions (C).