What is the solution to the system of equations?

x+y+3z=-4
2x-z=-3
-x-y-2z=5

a. (-1, -6, 1)
b. (1, -6, 1)
c. (-1, 6, 1)
d. (-1, -6, -1)

a

Step-by-step explanation:

Let's use the elimination method on equations 1 and 3 and see what happens:

x  +  y  +  3z  =  -4

-x  -  y  -  2z  =  5

It looks like both the x terms and the y terms cancel out leaving us with the fact that z = 1.  

Let's go back to the second equation now and sub in a 1 for z:

2x  -  z  =  -3 implies  2x - 1 = -3 and x = -1.

Pick any equation now to sub in the known values to find y.  I chose the first one, just because:

x + y + 3z = -4 implies -1 + y + 3(1) = -4 and

-1 + y + 3 = -4 so

y + 2 = -4 and

y = -6

So the solution set is (-1, -6, 1)

answer:   rotate 270° clockwise about (7, 1) and reflect across the line x = 7

step-by-step explanation:

because i took test

answer: the distance

step-by-step explanation:

to calculate the distance d of a line segment with endpoints (x1, y1) and (x2, y2) use the formula d (x2 x1)2 (y2 y1)2. to calculate the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) use the formula