Question

A little confused on how to do this one...

Solve the system by substitution.
{ 2x - y + z = -4
{ z = 5
{ -2x + 3y - z = -10

Help please. :P

Answer 1

2x - y + z = -4 .....now sub in 5 for z
2x - y + 5 = -4
2x - y = -4 - 5
2x - y = -9

2x + 3y - z = -10 ....sub in 5 for z
2x + 3y - 5 = -10
2x + 3y = -10 + 5
2x + 3y = -5

now we have :
2x - y = -9 --- multiply by -1
2x + 3y = -5
------------
-2x + y = 9 (result of multiplying by -1)
2x + 3y = -5
------------add
4y = 4
y = 1

now use an original equation and sub in known values to find x
2x - y + z = -4
2x - 1 + 5 = -4
2x + 4 = -4
2x = -4 - 4
2x = -8
x = -4

check..
2x + 3y - z = -10
2(-4) + 3(1) - 5 = -10
-8 + 3 - 5 = -10
-13 + 3 = -10
-10 = -10 (correct)

x = -4, y = 1, and z = 5