482,385 views
12 votes
12 votes
. Solve the system of equations using the Elimination Method.

X+3y - 2z=2
3x+2y+z=13
-2x+3y - 3z= -5

User Martin Wedvich
by
2.3k points

1 Answer

14 votes
14 votes

Answer:

{x,y,z}={1,3,4}

Explanation:

System of Linear Equations given :

[1] x + 3y - 2z = 2

[2] 3x + 2y + z = 13

[3] -2x + 3y - 3z = -5

Solve by Substitution :

// Solve equation [2] for the variable z

[2] z = -3x - 2y + 13

// Plug this in for variable z in equation [1]

[1] x + 3y - 2•(-3x-2y+13) = 2

[1] 7x + 7y = 28

// Plug this in for variable z in equation [3]

[3] -2x + 3y - 3•(-3x-2y+13) = -5

[3] 7x + 9y = 34

// Solve equation [3] for the variable y

[3] 9y = -7x + 34

[3] y = -7x/9 + 34/9

// Plug this in for variable y in equation [1]

[1] 7x + 7•(-7x/9+34/9) = 28

[1] 14x/9 = 14/9

[1] 14x = 14

// Solve equation [1] for the variable x

[1] 14x = 14

[1] x = 1

// By now we know this much :

x = 1

y = -7x/9+34/9

z = -3x-2y+13

// Use the x value to solve for y

y = -(7/9)(1)+34/9 = 3

// Use the x and y values to solve for z

z = -3(1)-2(3)+13 = 4

Solution :

{x,y,z} = {1,3,4}

User Cory Duncan
by
2.9k points