Solve.
-x + y + z = 7 x - y + 2z = 7
5x + y + z = 11
A)(1, 4, 2)
B)(1, 2, 4)
C)(4, 1, 2)
D)(4, 2, 1)

Question

Quizplus · Accepted Answer

We can solve this system using substitution or elimination. Here, we will use elimination. Adding the first two equations together eliminates y:
2x + 3z = 14
Multiplying the first equation by 5 and adding it to the third equation eliminates y again:
6x + 6z = 46
Now we have two equations in terms of only x and z. Solving this system gives us:
x = 1
z = 2
Substituting these values back into any of the three original equations gives us y = 4. Therefore, the solution is (1, 2, 4), which corresponds to answer choice (B). We can solve this system by using elimination or substitution method. Here is the solution using elimination:
First, we can add the first two equations to eliminate y:
x + y + z = 7
x - y + 2z = 7
-------------
2x + 3z = 14
Next, we can multiply the second equation by 5 and subtract the first equation to eliminate y again:
5x - 5y + 10z = 35
- (x + y + z = 7)
-------------
4x + 9z = 28
Now we have two equations with two variables:
2x + 3z = 14
4x + 9z = 28
We can multiply the first equation by 2 and subtract it from the second equation to eliminate x:
4x + 9z = 28
- (4x + 6z = 28)
-----------
3z = 0
z = 0
Substitute z = 0 into the first equation to solve for x:
2x + 3z = 14
2x + 3(0) = 14
2x = 14
x = 7
Finally, substitute x = 7 and z = 0 into any of the three equations to solve for y:
x + y + z = 7
7 + y + 0 = 7
y = 0
Therefore, the solution is (x, y, z) = (7, 0, 0), which corresponds to choice B.

Solve. -X + Y + Z = 7 X - Y