System of Equations

Question

Identify the number of solutions of the system of linear equations.

x + y + z = 2

2x - 3y + z = 11

-3x + 2y - 2z = -13

Answer 1

x + y + z = 2

2x - 3y + z = 11

-3x + 2y = -11

-2 eq1 + eq2;

3 eq1 + eq3:

x + y + z = 2

-5y -z = 7

5y + 3z= -5

adds the middle and last equations:

2z = 2

z = 1

the forces 5y = -8 and -5y = 8

y = -8/5

original first equation says:

x + -8/5 + 1 = 2

x + -3/5 = 2

x = 13/5

Answer 2

Subtracting the second equation from the first, we have the two remaining equations:

-x + 4y = -9

-3x + 2y = -11

Now, subtracting two times the second equation from the first, we have:

5x = 13

x = 13/5

Therefore, the system of equations has exactly one solution.