Question

Please help.What is the solution to the system of equations?

2x - 3y -2z=-7

x-3y-3z=4

x-2y-z=-3

a.(–8, –1, 3)
b.(–8, –1, –3)
c.(–8, 1, –3)
d.(8, –1, –3)

Answer 1

elimination method ....are you familiar with this ?

Answer 2

2x - 3y - 2z = -7
x - 3y - 3z = 4 -->(-2)
---------------
2x - 3y - 2z = -7
-2x + 6y + 6z = -8 (result of multiplying by -2)
---------------add
0 + 3y + 4z = - 15
3y + 4z = -15

x - 3y - 3z = 4 -->(-1)
x - 2y - z = -3
-----------------
-x + 3y + 3z = -4 (result of multiplying by -1)
x - 2y - z = -3
-----------------add
0 + y + 2z = -7
y + 2z = -7

3y + 4z = -15
y + 2z = -7 -->(-2)
----------------
3y + 4z = -15
-2y - 4z = 14 (result of multiplying by -2)
----------------add
y = -1

now sub -1 in for y
y + 2z = -7
-1 + 2z = -7
2z = -7 + 1
2z = -6
z = -3

now sub known values into one of the original equations
2x - 3y - 2z = -7
2x - 3(-1) - 2(-3) = -7
2x + 3 + 6 = -7
2x + 9 = -7
2x = -9 -7
2x = - 16
x = -8

lets check our answers...
x - 3y - 3z = 4
-8 - 3(-1) - 3(-3) = 4
-8 + 3 + 9 = 4
-8 + 12 = 4
4 = 4 (correct)

answer : x = -8, y = -1, z = -3 or (-8,-1,-3)

Answer 3

Thank you

Answer 4

your welcome :)

Answer 5

make two equations by eliminating any variable say x from three equations, taken two at a time.then solving for y and z from the two equations. finally substitute in any one of the original three equations and get the value of x

Answer 6

you do have to be real careful with elimination because it is easy to make mistakes.