Question

Pls help-

Solve the system of equations by transforming a matrix representing the system of equations into reduced row echelon form.

x+3y−3z=−27
2x+y+z=−2
x−y+3z=17

Answer 1

10x + 3y = 18

Explanation:

Step 1: Multiply equation (2) by 3 to eliminate the variable z:

6x + 3y + 3z = -6

Step 2: Add equation (1) and equation (4) together to eliminate the variable z:

x + 3y - 3z + 6x + 3y + 3z = -27 + (-6)

7x + 6y = -33 ...(5)

Step 3: Multiply equation (3) by 3 to eliminate the variable z:

3x - 3y + 9z = 51 ...(6)

Step 4: Add equation (5) and equation (6) together to eliminate the variable z:

7x + 6y + 3x - 3y + 9z = -33 + 51

10x + 3y = 18 ...(7)

Step 5: Solve equations (5) and (7) as a system of equations using either substitution or elimination method.

Step 6: Multiply equation (5) by 3 and equation (7) by 6 to eliminate the variable y:

30x + 9y = 54 ...(8)

60x + 18y = 108 ...(9)

Step 7: Subtract equation (8) from equation (9) to eliminate the variable y:

60x + 18y - 30x - 9y = 108 - 54

30x + 9y = 54 ...(10)

Step 8: Divide equation (10) by 3 to simplify the equation:

10x + 3y = 18 ...(11)

Step 9: Notice that equations (7) and (11) are the same. This means that we have redundant information and the system of equations is dependent. There are infinitely many solutions to this system.

In summary, the system of equations has infinitely many solutions, meaning that there are multiple values of x, y, and z that satisfy all three equations simultaneously.

Yes i am a student, im just smart, lol