What is the solution to the system of equations shown below?
2x + y -­ 3z = 11
­-x + 2y + 4z = -­3
x ­- 5y + 2z = ­- 18
a. ­(-1, 1, ­-4)
b, (1, 3, ­-2)
c.(3, 8, 1)
d. (2, -­3, 0)

  b.  (1, 3, ­-2)

Step-by-step explanation:

A graphing calculator or scientific calculator can solve this system of equations for you, or you can use any of the usual methods: elimination, substitution, matrix methods, Cramer's rule.

It can also work well to try the offered choices in the given equations. Sometimes, it can work best to choose an equation other than the first one for this. The last equation here seems a good one for eliminating bad answers:

  a: -1 -5(1) +2(-4) = -14 ≠ -18

  b: 1 -5(3) +2(-2) = -18 . . . . potential choice

  c: 3 -5(8) +2(1) = -35 ≠ -18

  d: 2 -5(-3) +2(0) = 17 ≠ -18

This shows choice B as the only viable option. Further checking can be done to make sure that solution works in the other equations:

  2(1) +(3) -3(-2) = 11 . . . . choice B works in equation 1

  -(1) +2(3) +4(-2) = -3 . . . choice B works in equation 2

constant acceleration- a

constant velocity- c

no velocity or acceleration- b

explanation:

for body moving with a constant acceleration, the rate of change of displacement changes over time. this is proven by the increasing gradient of the curve (a) against time.

a body that is moving at constant velocity covers equal distances over equal periods of time, thus the straight line with a constant gradient c.

a stationary body   covers no displacement as time elapses. thus the flat line with   zero gradient.