Solve the given system of equations 3x y 7 1 15x 5y z 12 22

Solve the given system of equations 3x y 7 (1) 15x 5y z 12 (22) Select the correct choice below and fill in any answer boxes within your choice O A. The solutio and y (Type integers or simplified fractions. n ISX O B. There are infinitely many solutions. Using ordered pairs, they can be expressed as (x l x y any real number (Simplify your answer. Type an expression using y as the variable as needed O C. There is no solution

Solution

1

-1

0

1

3

0

-5

12

0

3

1

9

To solve the given system of equations, we will reduce A to its RREF as under:

Add -3 times the 1st row to the 2nd row

Multiply the 2nd row by 1/3

Add -3 times the 2nd row to the 3rd row

Multiply the 3rd row by 1/6

Add 5/3 times the 3rd row to the 2nd row

Add 1 times the 2nd row to the 1st row

Then the RREF of A is

1

0

0

4

0

1

0

3

0

0

1

0

Hence the solution is x =4,y=3 and z = 0. Option A.

Note:

We can also solve the given system of equations by elimination and substitution.

1	-1	0	1
3	0	-5	12
0	3	1	9