Solve the system, if possible. (If the system is inconsistent, enter INCONSISTENT. If the system is dependent, enter a general solution in terms of x, y, or z.)
x + y = 18
y + z = 18
x − z = 0
The last equation means y = z so use it
x + z = 18
y + z = 18
-------------
x - y = 0
so
x = y
so
x = y = z = 9
the answer didn't work...
i think you used the wrong one for the third line...
x+z=18
y+z=18
x-z=0
9+9 = 18
9+9 = 18
9-9 = 0
That worked
However it is trivial
yes, x - z = 0
also x - y = 0
in fact x y and z are all 9
its saying its wrong? :/
By the way, the system is indeterminant. The determinant of the coefficient matrix is zero.
Well, if you are given choices say inconsistent. I used logic and not linear algebra to say 9,9,9
i have no clue why its not working...
i tried:
0,0,0
9,9,9
INCONSISTENT
To solve this system of equations, we can use the method of substitution or elimination to find the values of x, y, and z. Let's use the method of elimination.
First, let's add the first equation (x + y = 18) and the third equation (x - z = 0) together. This will eliminate the x term.
(x + y) + (x - z) = 18 + 0
2x + y - z = 18
Now, let's compare this new equation with the second equation (y + z = 18). Notice that the left-hand side of both equations match, which means the right-hand side must also match. Therefore, we can set the right-hand sides equal to each other and solve for y:
2x + y - z = y + z
2x - 2z = 2y
x - z = y
Now we have:
x - z = y (Equation 1)
y + z = 18 (Equation 2)
We can substitute Equation 2 into Equation 1:
x - z = y
x - z = y + z (since y + z = 18)
x = 2z + 18
We now have expressions for x and y in terms of z:
x = 2z + 18
y = x - z
To find a general solution, we need to express x, y, and z in terms of a parameter. Let's use z as the parameter:
x = 2z + 18
y = (2z + 18) - z
y = z + 18
Therefore, the general solution in terms of z is:
x = 2z + 18
y = z + 18
z = z
The system is dependent since it has infinitely many solutions.