Question

Solve for (x,y,z)
x + 5y + 5z = -10
x + y +z= 2
x + 2y + 3z = -3​

Answer 1

• (5, -1, -2)

Explanation:

Given system:

• x + 5y + 5z = -10
• x + y + z = 2
• x + 2y + 3z = -3​

Eliminate one of the variables.

Subtract the second equation from the first and from the third equation:

• x + 5y + 5z - x - y - z = -10 - 2 ⇒ 4y + 4z = -12 ⇒ y + z = -3
• x + 2y + 3z - x - y - z = -3 - 2 ⇒ y + 2z = -5

Now subtract the first equation above from the second to solve for z:

• y + 2z - y - z = -5 + 3
• z = -2

Find y:

• y + z = -3
• y - 2 = -3
• y = 2 - 3
• y = -1

Now find x:

• x + y + z = 2
• x - 1 - 2 = 2
• x - 3 = 2
• x = 2 + 3
• x = 5

The solution is:

• (5, -1, -2)