Answer:
Inconsistent
Step-by-step explanation:
a) Given:
x + y + z = -1 . . .(1)
y - 3z = 11 . . . (2)
2x + y + 5z = -12 . . .(3)
To find:
If the solution of the system of equations is either consistent dependent solution or an inconsistent one
We need to solve the system of equations. From equation (2), we will make y the subject of formula:
y = 11 + 3z (2*)
Substitute for y with 11 + 3z in both equation (1) and (2):
For equation 1: x + 11 + 3z + z = -1
x + 11 + 4z = -1
x + 4z = -1-11
x + 4z = -12 . . . (4)
For equation 3: 2x + 11 + 3z + 5z = -12
2x + 11 + 8z = -12
2x + 8z = -12-11
2x + 8z = -23 . . .(5)
We need to solve for x and z in equations (4) and (5)
Using elimination method:
To eliminate a variable, its coefficient needs to be the same in both equations
Let's eliminate x. We will multiply equation (4) by 2:
2x + 8z = -24 . . . (4*)
Now both equations have the same coefficient of x. Subtract equation (4) from (5):
2x - 2x + 8z - 8z = -23 - (-24)
0 + 0 = -23 + 24
0 = 1
Let hand side is not the same as right hand side.
When the left hand side is not equal to right hand side, the solution is said to be inconsistent or no sloution.
Your answer is inconsistent