If x-y+z=-1, -x+y+z=1, and x+y-z=-1, then x+y+z=?
A. -2
B. -1
C. 0
D. 1
E. 2
The OA is B.
I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.
If x-y+z=-1, -x+y+z=1, and x+y-z=-1, then x+y+z=?
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Adding together the 3 equations, we get:LUANDATO wrote:If x-y+z=-1, -x+y+z=1, and x+y-z=-1, then x+y+z=?
A. -2
B. -1
C. 0
D. 1
E. 2
(x-y+z) + (-x+y+z) + (x+y-z) = (-1) + 1 + (-1)
(x-x+x) + (-y+y+y) + (z+z-z) = -1
x + y + z = -1.
The correct answer is B.
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We could also invoke the Lazy Testwriter Principle: the answers are probably friendly and/or small numbers, so try those.
Let's start with
x-y+z=-1
This looks like -1 - 0 + 0, so let's say x = -1, y = 0, and z = 0. If we plug those into our other two equations:
-x + y + z =>
-(-1) + 0 + 0 => 1
and
x + y - z =>
-1 + 0 - 0 => -1
They both check out, so we're set!
Let's start with
x-y+z=-1
This looks like -1 - 0 + 0, so let's say x = -1, y = 0, and z = 0. If we plug those into our other two equations:
-x + y + z =>
-(-1) + 0 + 0 => 1
and
x + y - z =>
-1 + 0 - 0 => -1
They both check out, so we're set!
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Hi LUANDATO,If x-y+z=-1, -x+y+z=1, and x+y-z=-1, then x+y+z=?
A. -2
B. -1
C. 0
D. 1
E. 2
The OA is B.
I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.
Let's take a look at your question.
$$x-y+z=-1 ... (i)$$
$$-x+y+z=1... (ii)$$
$$x+y-z=-1 ... (iii)$$
$$x+y+z=?$$
Adding equations (i), (ii) and (iii),
$$\left(x-y+z\right)+\left(-x+y+z\right)+\left(x+y-z\right)=-1+1-1$$
$$x-y+z-x+y+z+x+y-z=0-1$$
$$x-x+x-y+y+y+z+z-z=-1$$
$$x+y+z=-1$$
Therefore, Option B is correct.
Hope it helps.
I am available if you'd like any follow up.
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Adding the 3 equations together, we have:BTGmoderatorLU wrote:If x-y+z=-1, -x+y+z=1, and x+y-z=-1, then x+y+z=?
A. -2
B. -1
C. 0
D. 1
E. 2
The OA is B.
x + y + z = -1 + 1 - 1
x + y + z = -1
Answer: B
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