Answer:
x = -4,
y = 3,
z = 2
Explanation:
{2x - y + z = -9,
{3x + 2y - 4z = -14
{x + z = -2;
First, let's make x the subject from the 3rd equation:
x = -2 - z
Replace x in the 1st and the 2nd equations with its value from the 3rd equation:
{2 * (-2 - z) - y + z = -9,
{3 * (-2 - z) + 2y - 4z = -14;
Now, we have a new system of equations
Let's eliminate the brackets (multiply every term inside the bracket by the term on the outside):
{-4 - 2z - y + z = -9,
{-6 - 3z + 2y - 4z = -14;
Collect like-terms (also, when moving the terms to the other side, make sure to change their signs into the opposite of the previous ones):
{-y - z = -9 + 4,
{2y - 7z = -14 + 6;
.
{-y - z = -5,
{2y - 7z = -8;
Let's make y the subject from the 1st equation:
-y = -5 + z / : (-1)
y = 5 - z
Replace y in the 2nd equation with its value from the 1st one:
2 × (5 - z) - 7z = -8
Expand the brackets:
10 - 2z - 7z = -8
Collect like-terms:
-9z = -8 - 10
-9z = -18 / : (-9)
z = 2
y = 5 - 2 = 3
x = -2 - 2 = -4