SAT Math Question: Must have answer in 15 minutes?

Question

z=x-y+4
z=y-w-3
z=w-x+5

What is the value of z?
A. 2
B. 3
C. 4
D. 6
E. 12

The answer is D. How do I do this?

Answer 1

I disagree with the answer (it can't be D).

Add the three equations. That will eliminate w, x and y.
z = ..... x - y + 4
z = -w ... + y - 3
z =. w -x .... + 5
-----------------------
3z = ............. 6

What you'll have left is:
3z = 4 - 3 + 5
3z = 6
z = 2

Be careful not to forget that z + z + z = 3z, or to miss the negative sign in front of -3 in equation #2.

As a double-check, imagine the values of the other variables were:
w = 3
x = 6
y = 8

Then you have:
z = 6 - 8 + 4 --> 2
z = 8 - 3 - 3 --> 2
z = 3 - 6 + 5 --> 2

The system of equations in consistent with z = 2.

Answer:
A. 2

Answer 2

Add 1-st and 2-nd equations:

2z = x - w + 1

and add to 3-rd:

3z = 6 => z = 2.

The answer is A.

Answer 3

z=x-y+4 ---(1)
z=y-w-3 ---(2)
z=w-x+5 => x-w=5-z

(1)+(2): 2z = x-w+1
=> 2z = (5-z)+1
=> 2z = 5 - z + 1
=> 3z = 6
=> z = 2
The answer is A.

Answer 4

Several people gave you the right answer in telling you the answer is A within the 15 minutes requested.

I don't know where you got that the answer was D.

At any rate, You should give one of them props for giving the best answer. Instead of withholding the points and making it go to voting.

Answer 5

z=x-y+4 let this be eq 1
z=y-w-3 let this be eq2
z=w-x+5 let this be eq 3

In eq 2
z=y-w-3
z+w=y-3

in eq 3
z=w-x+5
z-w=-x+5

now add eq 2 & 3
z+w=y-3
z-w=-x+5
------------------------
2z=0w=y-x+2
2z-2=y-x
-2z+2=x-y

now in eq1 substitute the value of x-y

z=x-y+4
z=-2z+2+4
z=-2z+6
z+2z=6
+3z=6
z=6/3
z=2

so teh answer is A

Answer 6

add the 3 equations to get

3z = 6 ---> z =2

answer is A