273,376 views
33 votes
33 votes
-x+2y=-3 x-4y-z=42x -y+3z=0solve for x

User Dstrants
by
3.5k points

1 Answer

15 votes
15 votes

The given system of equations is expressed as

- x + 2y = - 3

x - 4y - z = 4

2x - y + 3z = 0

From the first equation,

x = 2y + 3

We would substitute x = 2y + 3 into the second and third equation.

Substituting into the second equation, it becomes

2y + 3 - 4y - z = 4

2y - 4y - z = 4 - 3

- 2y - z = 1 fourth equation

Substituting into the third equation, it becomes

2(2y + 3) - y + 3z = 0

4y + 6 - y + 3z = 0

4y - y + 3z = 0 - 6

3y + 3z = - 6 fifth equation

From the fourth equation,

z = - 2y - 1

Substituting z = - 2y - 1 into the fifth equation, it becomes

3y + 3(- 2y - 1) = - 6

3y - 6y - 3 = - 6

3y - 6y = - 6 + 3

- 3y = - 3

y = - 3/ - 3

y = 1

Substituting y = 1 into x = 2y + 3, it becomes

x = 2 * 1 + 3

x = 5

Substituting y = 1 into z = - 2y - 1,

z = - 2 * 1 - 1

z = - 2 - 1

z = - 3

Therefore,

x = 5, y = 1, z = - 3

User Valent Richie
by
3.1k points