Solve.
-x - z = -7 3x - y = -1
X + y + z = 18

Question

Quizplus · Accepted Answer

Using the first equation, we can solve for z in terms of x: z = x + 7. 
Substituting that into the third equation, we get: 
x + y + (x + 7) = 18 
Simplifying: 
2x + y = 11 
Now we have two equations: 
3x - y = -1 and 2x + y = 11. 
Solving for y in the second equation: y = 11 - 2x. 
Substituting that into the first equation: 
3x - (11 - 2x) = -1 
Simplifying: 
5x = 10 
x = 2 
Now we can use either equation to solve for y: 
2(2) + y = 11 
y = 7 
Finally, using the first equation to solve for z: 
2 - z = -7 
z = 9 
Therefore, the solution is (2, 7, 9), which corresponds to choice D. First, we can use the second equation to solve for y: y = 3x + 1. 
Substituting this and x - z = -7 into the third equation, we get:
x + (3x + 1) + z = 18
4x + z = 17
Solving for z in x - z = -7, we get z = x + 7. 
Substituting this into 4x + z = 17, we get:
4x + x + 7 = 17
5x = 10
x = 2
Substituting x = 2 into x - z = -7, we get z = 9. 
Substituting x = 2 and z = 9 into y = 3x + 1, we get y = 7.

Therefore, the solution is (2, 7, 9), so the answer is D.

Solve. -X - Z = -7 3x - Y = -1